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Several Relationships Connected to a Special Function Used in the Simple Equations Method (SEsM)

verfasst von : Nikolay K. Vitanov

Erschienen in: New Trends in the Applications of Differential Equations in Sciences

Verlag: Springer Nature Switzerland

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Abstract

The use of certain classes of simple equations in the Simple Equations Method (SEsM) favors the occurrence of a specific special function in these solutions. We discuss this special function and its specific cases and derive some relationships which connect the special functions possessing different parameters.

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Vorheriges Kapitel Physics Informed Cellular Neural Networks for Solving Partial Differential Equations

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Torokhti A., Howlett P.: Computational Methods for Modelling of Nonlinear Systems. Elsevier, Amsterdam (2007)

Nikolova, E. V.: On nonlinear waves in a blood-filled artery with an aneurysm. In AIP Conference Proceedings vol. 1978, 470050 (2018). https://doi.org/10.1063/1.5044120

Jordanov, I. P.: On the nonlinear waves in (2+ 1)-dimensional population systems. Compt. rend. Acad. bulg. Sci 61, 307–314 (2008).

Dimitrova, Z.I.: On travelling waves in lattices: the case of Riccati lattices. Journal of Theoretical and Applied Mechanics 42, 3-22 (2012), https://doi.org/10.2478/v10254-012-0011-2).

Jordanov, I., Nikolova, E.: On nonlinear waves in the spatio-temporal dynamics of interacting populations. Journal of Theoretical and Applied Mechanics 43, 69 – 76 (2013). https://doi.org/10.2478/jtam-2013-0015.

Jordanov, I. P., Dimitrova, Z. I.: On Nonlinear Waves of Migration. Journal of Theoretical and Applied Mechanics 40, 89–96 (2010).

Dimitrova, Z. I., Ausloos, M.: Primacy analysis in the system of Bulgarian cities. Open Physics 13, 218 – 225 (2015). https://doi.org/10.1515/phys-2015-0029

Nicolis G., Nicolis C.,: Foundations of Complex Systems. World Scientific, New Jersey (2012).

Dimitrova, Z. I.: Fluctuations and dynamics of the chaotic attractor connected to an instability in a heated from below rotating fluid layer. Compt. rend. Acad. bulg. Sci 60, 1065 – 1070 (2007).

10.

Ivanova, K., Ausloos, M.: Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking. Physica A: Statistical Mechanics and its Applications 274, 349-354 (274). https://doi.org/10.1016/S0378-4371(99)00312-X

11.

Vitanov N.K.: Science Dynamics and Research Production. Indicators, Indexes, Statistical Laws and Mathematical Models. Springer, Cham (2016)

12.

Nikolova, E. V., Serbezov, D. Z., Jordanov, I.: Nonlinear spread waves in population dynamics including a human-induced Allee effect. AIP Conference Proceedings vol. 2075, 150004 (2019). https://doi.org/10.1063/1.5091327

13.

Levin. R.: Complexity. Life at the Edge of Chaos. The University of Chicago Press, Chicago (1999).

14.

Vitanov, N. K., Ausloos, M., Rotundo, G.: Discrete model of ideological struggle accounting for migration. Advances in Complex Systems 15, 1250049 (2012). https://doi.org/10.1142/S021952591250049X

15.

Dimitrova, Z. I., Hoffmann N. P.: On the probability for extreme water levels of the river Elba in Germany. Compt. rend. Acad. bulg. Sci 65, 153 – 160 (2012).

16.

Vitanov, N. K., Vitanov, K. N.: Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration. Physica A: Statistical Mechanics and its Applications 509, 635-650 (2018). https://doi.org/10.1016/j.physa.2018.06.076

17.

Vitanov, N. K., Vitanov, K. N.: Box model of migration channels. Mathematical Social Sciences 80, 108 – 114 (2016). https://doi.org/10.1016/j.mathsocsci.2016.02.001

18.

Dimitrova, Z.I.: On the nonlinear dynamics of interacting populations. Effects of delay on populations substitution. Compt. rend. Acad. bulg. Sci 61, 1541 – 1548 (2008).

19.

Vitanov, N. K., Vitanov, K. N.: On the motion of substance in a channel of a network and human migration. Physica A: 490, 1277-1294 (2018). https://doi.org/10.1016/j.physa.2017.08.038

20.

Jordanov, I. P., Nikolova, E. V.: On the evolution of nonlinear density population waves in the socio-economic systems. AIP Conference Proceedings vol. 2075, 150002 (2019). https://doi.org/10.1063/1.5091325

21.

Dimitrova, Z. I. Flows of substances in networks and network channels: Selected results and applications. Entropy, 24, 1485, (2022). https://doi.org/10.3390/e24101485.

22.

Chen, W.-K.: Theory of Nets. Flows in Networks. Imperial College Press, London, UK (2003)

23.

Struble R.: Nonlinear Differential Equations. Dover, New York (2018)

24.

Kantz, H., Schreiber T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge, UK (2004)

25.

Vitanov, N. K.: Upper bounds on the heat transport in a porous layer. Physica D 136, 322-339 (2000). https://doi.org/10.1016/S0167-2789(99)00165-7

26.

Dimitrova, Z., Gogova, D.,: Investigation of Differences in Optical Phonons Modes by Principal Component Analysis. Compt. rend. Acad. bulg. Sci 63, 1415 – 1420 (2010).

27.

Vitanov, N. K., Ausloos, M. R.: Knowledge epidemics and population dynamics models for describing idea diffusion. In: Scharnhorst A., Boerner K., van den Besselaar P. (eds.) Models of science dynamics. Understanding Complex Systems. pp. 69-125. Springer, Berlin, Heidelberg (2012). https://doi.org/10.1007/978-3-642-23068-4_3

28.

Dimitrova, Z. I., Vitanov, N. K.: Adaptation and its impact on the dynamics of a system of three competing populations. Physica A: Statistical Mechanics and its Applications 300, 91-115 (2001). https://doi.org/10.1016/S0378-4371(01)00330-2

29.

Mills T.: Applied Time Series Analysis. Academic Press, London (2019)

30.

Dimitrova, Z. I., Vitanov, N. K.: Chaotic pairwise competition. Theoretical Population Biology 66, 1-12 (2004). https://doi.org/10.1016/j.tpb.2003.10.008

31.

Dimitrova, Z. I.: On the Low-Dimensional Dynamics of Blood Flow in Small Peripheral Human Arteries. Compt. rend. Acad. bulg. Sci. 63, 55 – 60 (2010).

32.

Vitanov, N. K., Vitanov, K. N.: Statistical distributions connected to motion of substance in a channel of a network. Physica A 527, 121174 (2019). https://doi.org/10.1016/j.physa.2019.121174

33.

Borisov, R., Dimitrova, Z. I., Vitanov, N. K.: Statistical characteristics of stationary flow of substance in a network channel containing arbitrary number of arms. Entropy 22, 553 (2020). https://doi.org/10.3390/e22050553

34.

Dimitrova, Z. I., Vitanov, K. N.: Homogeneous balance method and auxiliary equation method as particular cases of simple equations method (SEsM). In AIP Conference Proceedings vol. 2321, 030004 (2021). https://doi.org/10.1063/5.0043070

35.

Vitanov, N. K., Vitanov, K. N., Kantz, H.: On the motion of substance in a channel of a network: Extended model and new classes of probability distributions. Entropy 22, 1240 (2020). https://doi.org/10.3390/e22111240

36.

Hopf E.: The partial differential equation \(u_t+u u_x = u_{xx}\). Communications on Pure and Applied Mathematics 3, 201 – 230 (1950). https://doi.org/10.1002/cpa.3160030302

37.

Cole, J. D.: On a quasi-linear parabolic equation occurring in aerodynamics. Quarterly of applied mathematics 9, 225 – 236 (1951). https://doi.org/10.1090/QAM/42889

38.

Ablowitz, M. J., Kaup, D. J., Newell, A. C., Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Studies in Applied Mathematics 53, 249-315 (1974). https://doi.org/10.1002/sapm1974534249

39.

Gardner, C. S., Greene, J. M., Kruskal, M. D., Miura, R. M.: Method for solving the Korteweg-deVries equation. Physical review letters 19, 1095 – 1097 (1967). https://doi.org/10.1103/PhysRevLett.19.1095

40.

Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, Cambridge, UK, (2004)

41.

Tabor. M.: Chaos and Integrability in Dynamical Systems. Wiley, New York (1989)

42.

Weiss, J., Tabor, M., Carnevale, G.: The Painlevé property for partial differential equations. Journal of Mathematical Physics 24, 522-526 (1983). https://doi.org/10.1063/1.525721

43.

Kudryashov, N. A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons & Fractals 24, 1217-1231 (2005). https://doi.org/10.1016/j.chaos.2004.09.109

44.

Kudryashov, N. A., Loguinova, N. B.: Extended simplest equation method for nonlinear differential equations. Applied Mathematics and Computation 205, 396 – 402 (2008). https://doi.org/10.1016/j.amc.2008.08.019

45.

Kudryashov, N. A.: Exact solitary waves of the Fisher equation. Physics Letters A 342, 99-106 (2005). https://doi.org/10.1016/j.physleta.2005.05.025

46.

Kudryashov, N. A.: Exact solutions and integrability of the Duffing-Van der Pol equation. Regular and Chaotic dynamics 23, 471-479 (2018). https://doi.org/10.1134/S156035471804007X

47.

Vitanov, N. K., Dimitrova, Z. I., Vitanov, K. N.: Simple Equations Method (SEsM): Algorithm, connection with Hirota method, Inverse Scattering Transform Method, and several other methods. Entropy 23, 10 (2021). https://doi.org/10.3390/e23010010

48.

Vitanov, N. K.: Recent developments of the methodology of the modified method of simplest equation with application. Pliska Studia Mathematica Bulgarica 30, 29 – 42 (2019).

49.

Vitanov, N.K.: Modified method of simplest equation for obtaining exact solutions of nonlinear partia differential equations: history, recent developments of the methodology and studied of classes of equations. Journal of Theoretical and Applied Mechanics 49, 107 – 122 (2019).

50.

Vitanov, N. K.: The simple equations method (SEsM) for obtaining exact solutions of nonlinear PDEs: Opportunities connected to the exponential functions. AIP Conference Proceedings vol. 2159, 030038 (2019). https://doi.org/10.1063/1.5127503

51.

Vitanov, N. K., Dimitrova, Z. I.: Simple equations method (SEsM) and other direct methods for obtaining exact solutions of nonlinear PDEs. AIP Conference Proceedings vol. 2159, 030039 (2019). https://doi.org/10.1063/1.5127504

52.

Dimitrova, Z. I., Vitanov, N. K.: Travelling waves connected to blood flow and motion of arterial walls. Gadomski, A. (ed.) In: Water in Biomechanical and Related Systems pp. 243-263. Springer, Cham. (2021)

53.

Martinov, N., Vitanov, N.: On the correspondence between the self-consistent 2D Poisson-Boltzmann structures and the sine-Gordon waves. Journal of Physics A: Mathematical and General 25, L51 – L56 (1992). https://doi.org/10.1088/0305-4470/25/2/004

54.

Martinov, N., Vitanov, N.: On some solutions of the two-dimensional sine-Gordon equation. Journal of Physics A: Mathematical and General 25, L419 – L426 (1992). https://doi.org/10.1088/0305-4470/25/8/007

55.

Martinov, N. K., Vitanov, N. K.: New class of running-wave solutions of the (2+ 1)-dimensional sine-Gordon equation. Journal of Physics A: Mathematical and General 27, 4611 – 4618 (1994). https://doi.org/10.1088/0305-4470/27/13/034

56.

Martinov, N. K., Vitanov, N. K.: On self-consistent thermal equilibrium structures in two-dimensional negative-temperature systems. Canadian Journal of Physics 72, 618 – 624 (1994). https://doi.org/10.1139/p94-079

57.

Vitanov, N. K.: Breather and soliton wave families for the sine-Gordon equation. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 2409 – 2423 (1998). https://doi.org/10.1098/rspa.1998.0264

58.

Vitanov, N. K., Martinov, N. K.: On the solitary waves in the sine-Gordon model of the two-dimensional Josephson junction. Zeitschrift fur Physik B Condensed Matter 100, 129 – 135 (1996). https://doi.org/10.1007/s002570050102

59.

Vitanov, N. K.: On travelling waves and double-periodic structures in two-dimensional sine-Gordon systems. Journal of Physics A: Mathematical and General 29, 5195 – 5207 (1996). https://doi.org/10.1088/0305-4470/29/16/036

60.

Vitanov, N. K., Jordanov, I. P., Dimitrova, Z. I.: On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations. Communications in Nonlinear Science and Numerical Simulation 14, 2379 – 2388 (2009). https://doi.org/10.1016/j.cnsns.2008.07.015

61.

Vitanov, N. K., Jordanov, I. P., Dimitrova, Z. I.: On nonlinear population waves. Applied Mathematics and Computation 215, 2950 – 2964 (2009). https://doi.org/10.1016/j.amc.2009.09.041

62.

Vitanov, N. K.: Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity. Communications in Nonlinear Science and Numerical Simulation 15, 2050 – 2060 (2010). https://doi.org/10.1016/j.cnsns.2009.08.011

63.

Vitanov, N. K., Dimitrova, Z. I.: Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics. Communications in Nonlinear Science and Numerical Simulation 15, 2836 – 2845 (2010). https://doi.org/10.1016/j.cnsns.2009.11.029

64.

Vitanov, N. K., Dimitrova, Z. I., Kantz, H.: Modified method of simplest equation and its application to nonlinear PDEs. Applied Mathematics and Computation 216, 2587 – 2595 (2010). https://doi.org/10.1016/j.amc.2010.03.102

65.

Vitanov, N. K.: Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs. Communications in Nonlinear Science and Numerical Simulation 16, 1176 – 1185 (2011). https://doi.org/10.1016/j.cnsns.2010.06.011

66.

Vitanov, N. K., Dimitrova, Z. I., Vitanov, K. N.: On the class of nonlinear PDEs that can be treated by the modified method of simplest equation. Application to generalized Degasperis-Processi equation and b-equation. Communications in Nonlinear Science and Numerical Simulation 16, 3033 – 3044 (2011). https://doi.org/10.1016/j.cnsns.2010.11.013

67.

Vitanov, N. K.: On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: the role of the simplest equation. Communications in Nonlinear Science and Numerical Simulation 16, 4215 – 4231 (2011). https://doi.org/10.1016/j.cnsns.2011.03.035

68.

Vitanov, N. K.: On modified method of simplest equation for obtaining exact solutions of nonlinear PDEs: case of elliptic simplest equation. Pliska Studia Mathematica Bulgarica 21, 257 – 266 (2012).

69.

Vitanov, N. K., Dimitrova, Z. I., Kantz, H.: Application of the method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg-de Vries equation and generalized Camassa-Holm equation. Applied Mathematics and Computation 219, 7480 – 7492 (2013). https://doi.org/10.1016/j.amc.2013.01.035

70.

Vitanov, N. K., Dimitrova, Z. I., Vitanov, K. N.: Traveling waves and statistical distributions connected to systems of interacting populations. Computers & Mathematics with Applications 66, 1666 – 1684 (2013). https://doi.org/10.1016/j.camwa.2013.04.002

71.

Vitanov, N. K., Vitanov, K. N.: Population dynamics in presence of state dependent fluctuations. Computers & Mathematics with Applications 68, 962-971 (2014). https://doi.org/10.1016/j.camwa.2014.03.006

72.

Vitanov, N. K., Dimitrova, Z. I.: Solitary wave solutions for nonlinear partial differential equations that contain monomials of odd and even grades with respect to participating derivatives. Applied Mathematics and Computation 247, 213 – 217 (2014). https://doi.org/10.1016/j.amc.2014.08.101

73.

Dimitrova, Z.I.: Relation between G’/G-expansion method and the modified method of simplest equation. Compt. rend. Acad. bulg. Scie 65, 1513 – 1520 (2012).

74.

Vitanov, N. K., Dimitrova, Z. I., Vitanov, K. N.: Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications. Applied Mathematics and Computation 269, 363 – 378 (2015). https://doi.org/10.1016/j.amc.2015.07.060

75.

Vitanov, N. K., Dimitrova, Z. I., Ivanova, T. I.: On solitary wave solutions of a class of nonlinear partial differential equations based on the function 1/\(cosh^n\) (\(\alpha \)x+ \(\beta \)t). Applied Mathematics and Computation 315, 372 – 380 (2017). https://doi.org/10.1016/j.amc.2017.07.064

76.

Vitanov, N. K., Dimitrova, Z. I.: On the modified method of simplest equation and the nonlinear Schrödinger equation. Journal of Theoretical and Applied Mechanics 48, 59 – 68 (2018).

77.

Nikolova, E. V., Jordanov, I. P., Dimitrova, Z. I., Vitanov, N. K.: Evolution of nonlinear waves in a blood-filled artery with an aneurysm. AIP Conference Proceedings vol. 1895, 070002 (2017). https://doi.org/10.1063/1.5007391

78.

Jordanov, I.P., Vitanov, N.K.: On the Exact Traveling Wave Solutions of a Hyperbolic Reaction-Diffusion Equation. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. BGSIAM 2017. Studies in Computational Intelligence, vol. 793, pp. 199 – 210. Springer, Cham. (2019). https://doi.org/10.1007/978-3-319-97277-0_16

79.

Nikolova, E. V., Chilikova-Lubomirova, M., Vitanov, N. K.: Exact solutions of a fifth-order Korteweg-de Vries-type equation modeling nonlinear long waves in several natural phenomena. AIP Conference Proceedings vol. 2321, 030026 (2021). https://doi.org/10.1063/5.0040089

80.

Dimitrova, Z. I.: Several examples of application of the simple equations method (SEsM) for obtaining exact solutions of nonlinear PDEs. AIP Conference Proceedings vol. 2459, 030005 (2022). https://doi.org/10.1063/5.0083572

81.

Dimitrova, Z. I.: On several specific cases of the simple equations method (SEsM): Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method, general projective Riccati equations method, and first intergal method. AIP Conference Proceedings, vol. 2459, 030006 (2022). https://doi.org/10.1063/5.0083573

82.

Vitanov, N. K. Simple Equations Method (SEsM): An effective algorithm for obtaining exact solutions of nonlinear differential equations. Entropy, 24, 1653 (2022). https://doi.org/10.3390/e24111653

83.

Vitanov, N. K., Vitanov, K. N. Epidemic waves and exact solutions of a sequence of nonlinear differential equations connected to the SIR model of epidemics. Entropy, 25, 438 (2023) https://doi.org/10.3390/e25030438

84.

Vitanov, N. K., Dimitrova, Z. I. Computation of the exact forms of waves for a set of differential equations associated with the SEIR model of epidemics. Com- putation, 11, 129 (2023). https://doi.org/10.3390/computation11070129

85.

Vitanov, N. K. Simple equations method (SEsM) and nonlinear PDEs with fractional derivatives. AIP Conference Proceedings 2459, 030040 (2022). https://doi.org/10.1063/5.0083566

86.

Vitanov, N. K. Simple equations method (SEsM): Review and new results. AIP Conference Proceedings, 2459, 020003 (2022). https://doi.org/10.1063/5.0083565

87.

Vitanov, N.K. Simple Equations Method (SEsM): Areas of possible applications. Springer Proceedings in Mathematics & Statistics, 412, 15 - 24 (2023). https://doi.org/10.1007/978-3-031-21484-4_2

88.

Vitanov, N.K. Special Functions and polynomials connected to the Simple Equa- tions Method (SEsM). Springer Proceedings in Mathematics & Statistics, 412, 73 - 81 (2023). https://doi.org/10.1007/978-3-031-21484-4_7

89.

Nikolova, E.V., Chilikova-Lubomirova, M. Exact traveling wave solutions of the generalized Rosenau-Kawahara-RLW equation via Simple Equations Method. Springer Proceedings in Mathematics & Statistics, 412, 141 - 152 (2023). https://doi.org/10.1007/978-3-031-21484-413

90.

Nikolova, E. V. Exact travelling-wave solutions of the extended fifth- order Korteweg-de Vries equation via Simple Equations Method (SEsM): The case of two simple equations. Entropy, 24, 1288 (2022). https://doi.org/10.3390/e24091288

91.

Nikolova, E. V., Chilikova-Lubomirova, M . Exact traveling wave solutions of the Nikolaevskiy model for nonlinear seismic waves. AIP Conference Proceedings 2459, 030028 (2022). https://doi.org/10.1063/5.0083633

92.

Jordanov, I.P. An application of Simplest Equations Method to nonlinear equations of Schrödinger kind. Springer Proceedings in Mathematics & Statistics, 412, 187 – 197 (2023). https://doi.org/10.1007/978-3-031-21484-4_18

93.

Jordanov, I. P. Simple Equations Method applied to equations of nonlinear Schrödinger kind. AIP Conference Proceedings, 2459, 030016 (2022). https://doi.org/10.1063/5.0084340

94.

Vitanov, N. K., Dimitrova, Z. I., Vitanov, K. N.: On the use of composite functions in the Simple Equations Method to obtain exact solutions of nonlinear differential equations. Computation 9, 104 (2021). https://doi.org/10.3390/computation9100104

Titel: Several Relationships Connected to a Special Function Used in the Simple Equations Method (SEsM)
verfasst von: Nikolay K. Vitanov
Verlag: Springer Nature Switzerland
Buch: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_4

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