Top

Optical and Quantum Electronics

Published in:

01-08-2020

Optical propagation patterns in medium modeled by the generalized nonlinear Schrödinger equation

Authors: Ya-nan Liu, Chun-yan Wang

Published in: Optical and Quantum Electronics | Issue 8/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The propagation patterns of optical waves in medium which are described by the generalized nonlinear Schrödinger equation are studied in details. A varied of exact solutions are obtained, which include singular solution, solitary wave solution, periodic solution and double periodic solution. Under the concrete parameters, we analyze the modulus of solutions, from which we can get new propagation patterns.

previous article Quantum communication using code division multiple access network

next article Enhancing of multiwavelength free space optical communication system via optimizing the transceiver design parameters

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Ablowitz, M.J., Ablowitz, M.A., Prinari, B., Trubatch, A.D.: Discrete and Continuous nonlinear Schrödinger System, pp. 31–35. Cambridge University Press, Cambridge (2004)MATH

Anderson, D.: Variational approach to nonlinear pulse propagation in optical fibers. Phys. Rev. Lett. 27, 3135–3145 (1983)ADS

Bedaque, P.F., Braaten, E., Hammer, H.W.: Three-body recombination in Bose gases with large scattering length. Phys. Rev. Lett. 908, 50 (2000)

Benney, D.J., Newell, A.C.: Propagation of nonlinear wave envelopes. J. Math. Phys. 46, 133–139 (1967)MathSciNetMATH

Biondini, G., Kovačič, G.: Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions. J. Math. Phys. 55, 506 (2014)MATH

Biswas, A., Ekici, M.: Optical solitons in birefringent fibers with quadratic-cubic nonlinearity by extended Jacobi’s elliptic function expansion. Optik 178, 117–121 (2019)ADS

Gandarias, M.L., Bruzon, M.S.: Classical and nonclassical symmetries of a generalized Boussinesq equation. J. Math. Phys. 5, 8–12 (1998)MathSciNetMATH

Kai, Y.: The classification of the single travelling wave solutions to the variant Boussinesq equations. Pramana 87, 5912 (2016)

Kai, Y.: Exact solutions and asymptotic solutions of one-dimensional domain walls in nonlinearly coupled system. Nonlinear Dyn. 92, 1665–1677 (2018)

Kai, Y., et al.: Exact and asymptotic solutions to magnetohydrodynamic flow over a nonlinear stretching sheet with a power-law velocity by the homotopy renormalization method. Phys. Fluids 31, 63606 (2019)

Kanna, T., Lakshmanan, M.: Exact soliton solutions shape changing collisions and partially coherent solitons in coupled nonlinear Schrödinger equations. Phys. Rev. Lett. 49, 601–604 (2001)

Liu, C.S.: Trial equation method and its applications to nonlinear evolution equations. Acta Phys. Sin. 54, 2505–2509 (2005)MathSciNetMATH

Liu, C.S.: Using trial equation method to solve the exact solutions for two kinds of KdV equations with variable coefficients. Acta Phys. Sin. 54, 4506–4510 (2005)MATH

Liu, C.S.: All single traveling wave solutions to (3 + 1)-dimensional Nizhnok–Novikov–Veselov equation. Commun. Theor. Phys. 45, 991–992 (2006)ADSMathSciNet

Liu, C.S.: Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Comput. Phys. Commun. 45, 219–223 (2006)

Liu, C.S.: A new trial equation method and its applications. Commun. Theor. Phys. 45, 359–357 (2006)ADS

Liu, C.S.: Classification of all single travelling wave solutions to Calogero–Degasperis–Focas equation. Commun. Theor. Phys. 48, 601–604 (2007a)ADSMathSciNetMATH

Liu, C.S.: The classification of travelling wave solutions and superposition of multi-solutions to Camassa–Holm equation with dispersion. Chin. Phys. B 16, 1832 (2007b)

Liu, C.: The renormalization method based on the Taylor expansion and applications for asymptotic analysis. Nonlinear Dyn. 88, 1099–1124 (2007c)

Liu, C.S.: Representations and classification of traveling wave solutions to Sinh–Gordon equation. Commun. Theor. Phys. 49, 153–158 (2008)ADSMathSciNetMATH

Liu, C.S.: Solution of ODE \(u^{\prime \prime }+p(u)(u^{\prime })^{2}+q(u)=0\) and applications to classifications of all single travelling wave solutions to some nonlinear mathematical physics equations. Commun. Theor. Phys. 49, 291–296 (2008)ADSMathSciNetMATH

Liu, C.S.: Exponential function rational expansion method for nonlinear differential–difference equations. Chaos Soliton Fractals 40, 708–716 (2009)ADSMathSciNetMATH

Liu, C.S.: Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Comput. Phys. Commun. 181, 317–324 (2010)ADSMathSciNetMATH

Liu, C.: The essence of the generalized Newton binomial theorem. Commun. Nonlinear Sci. Numer. Simul. 15, 2766–2768 (2010)ADS

Liu, C.S.: Trial equation method based on symmetry and applications to nonlinear equations arising in mathematical physics. Found. Phys. 41, 793–804 (2011a)ADSMathSciNetMATH

Liu, Y.: Exact solutions to nonlinear Schrödinger equation with variable coefficients. Appl. Math. Comput. 217, 5866–5869 (2011b)

Liu, C.: The renormalization method from continuous to discrete dynamical systems: asymptotic solutions. reductions and invariant manifolds. Nonlinear Dyn. 94, 873–888 (2018)

Liu, C.S.: Exactly solving some typical Riemann–Liouville fractional models by a general method of separation of variables. Commun. Theor. Phys. 72(5), 055006 (2020)ADSMathSciNet

Liu, Y., Wang, X.: The construction of solutions to Zakharov–Kuznetsov equation with fractional power nonlinear terms. Adv. Differ. Equ. 2019, 134 (2019)MathSciNetMATH

Ma, W.X.: Integrability. In: Scott, A. (ed.) Encyclopedia of Nonlinear Science, pp. 250–253. Taylor-Francis, London (2005)

Ma, X.X.: Interaction solutions to the Hirota–Satsuma–Ito equation in (2 + 1)-dimensions. Front. Math. China 14, 619–629 (2019)MathSciNetMATH

Ma, W.X.: A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions. J. Appl. Anal. Comput. 9(4), 1319–1332 (2019)MathSciNet

Ma, W.X.: Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation. Mod. Phys. Lett. B 33, 1950457 (2019)ADSMathSciNet

Ma, X.X.: Inverse scattering for nonlocal reverse-time nonlinear Schrödinger equations. Appl. Math. Lett. 102, 106161–7 (2020)MathSciNetMATH

Ma, W.X., Lee, J.H.: A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo–Miwa equation. Chaos Solitons Fractals 42, 1356–1363 (2009)ADSMathSciNetMATH

Remoissenet, M.: Waves Called Solitons: Concepts and Experiments, vol. 3, pp. 98–100. Springer, Berlin (1999)MATH

Reyes, M.A., Guti, D.: Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations. Commun. Theor. Phys. 31, 20 (2016)

Seadawy, A.R.: Exact solutions of a two-dimensional nonlinear Schrödinger equation. Appl. Math. Lett. 25, 687–691 (2012)MathSciNetMATH

Seadawy, A.R.: Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method. Eur. Phys. J. Plus 130, 1–10 (2015)

Triki, H., Porsezian, K.: Bright and kink solitons in the quadratic-cubic nonlinear Schrödinger equation with time and space modulated nonlinearities and potentials. J. Mod. Optic 12, 1–9 (2017)

Wang, C.Y., Gao, W.J.: Asymptotic analysis of reduced Navier–Stokes equations by homotopy renormalization method. Rep. Math. Phys. 80, 29–37 (2017)ADSMathSciNetMATH

Wang, X., Liu, Y.: All single travelling wave patterns to fractional Jimbo–Miwa equation and Zakharov–Kuznetsov equation. Pramana-J. Phys. 92(3), 31 (2019)ADS

Wang, X., Liu, Y.: All envelop traveling wave patterns to nonlinear Schrödinger equation in parabolic law medium. Mod. Phys. Lett. B 33, 1850428 (2019)ADS

Yu, F.: Multi-rogue waves for a higher-order nonlinear Schrödinger equation in optical fibers. Appl. Math. Comput. 220, 176–184 (2013)MathSciNetMATH

Zeng, J., Malomed, B.A.: Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity. Phys. Rev. E 33, 103–107 (2012)

Title: Optical propagation patterns in medium modeled by the generalized nonlinear Schrödinger equation
Authors: Ya-nan Liu
Chun-yan Wang
Publication date: 01-08-2020
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 8/2020
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-020-02486-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 8/2020

Dynamics of quantum correlations for different types of noisy channels

Exception point induced flat-band and waveguide laser

Growth and investigations of 3rd order NLO properties of novel semi organic tartaric acid lithium sulfate single crystal for photonics application

Effect of device parameters on improving the quantum efficiency of a lateral Si p–i–n photodetector

Monolithic light emitting device and light detecting device fabricated with a commercial LED wafer

New compact of absorber thermal surface