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Optical and Quantum Electronics

Erschienen in:

01.02.2023

Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions

verfasst von: Syed T. R. Rizvi, Aly R. Seadawy, Sarfaraz Ahmed, Kashif Ali

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2023

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Abstract

The current study deals with investigation of Einstein’s vacuum field equation (EVFE) for exploring various lumps, breathers and interaction solutions via bilinear method and choosing appropriate polynomial function. In particular, we obtain lump, lump 1-strip, lump 2-strip, lump periodic, Manifold periodic, rogue wave (RW), generalized breather, Akhmediev breather, Ma breather, Kuznetsov-Ma breather and its corresponding RW solutions for ensuing model. In addition, we also made interaction among lump, periodic and kink-wave with their numeric simulation. In general relativity, the governing model play momentous part in many ambitious experiments and space missions. Furthermore, distinct other random parameters give enough choice to manipulate physical states governed by this model are observed.

Vorheriger Artikel Deep learning/Kalman filter-based underwater localization in VLC systems

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Ahmed, I., Seadawy, A.R., Dianchen, L.: Kinky breathers, W-shaped and multi-peak solitons interaction in \((2+1)\)-dimensional nonlinear Schrodinger’s equation with Kerr law of nonlinearity. Eur. Phys. J. Plus 134(120), 1–11 (2019)

Ahmed, S., Ashraf, R., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, A., El-Shehawi, A.M.: Lump, multi-wave, kinky breathers, interactional solutions and stability analysis for general \((2+ 1)\)-rth dispersionless Dym equation. Results Phys. 25, 104160 (2021)

Akram, U., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, S., Sayed, S.: Traveling wave solutions for the fractional Wazwaz–Benjamin–Bona–Mahony model in arising shallow water waves. Results Phys. 20, 103725 (2021)

Ali, I., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Ali, K.: Conserved quantities along with Painleve analysis and Optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model. Int. J. Mod. Phys. B 34(30), 2050283 (2020)ADSMathSciNetMATH

Aziz, N., Seadawy, A.R., Raza, U., Ali, K., Rizvi, S.T.: Chirped optical pulses for generalized longitudinal Lugiato Lefever: cubic nonlinear Schrödinger equation. Opt. Quantum Electron. 54, 649 (2022)

Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., El-Rashidy, K., Mahmoud, S.F.: Analytical wave structures in plasma physics modelled by Gilson–Pickering equation by two integration norms. Results Phys. 23, 103959 (2021)

Bronnikov, K.A., Santos, N.O., Wang, A.: Cylindrical systems in general relativity. Class. Quantum Grav. 37(11), 113002 (2020)ADSMathSciNetMATH

Crothers, S.J.: On the general solution to Einstein’s vacuum field and its implications for relativistic degeneracy. J. Adv. Stud. Theor. Exp. Phys., Incl. Relat. Themes Math. 205(1), 10 (1927)

Debnath, P., Ishwarchandra, N.: The study of the energy conditions of the universe and unique solutions of the Einstein’s field equations in the lights of the theory of general relativity. Indian J. Sci. Technol. 14(36), 2826–2831 (2021)

Dudley, J.M., Genty, G., Dias, F., Kibler, B., Akhmediev, N.: Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation. Opt. Express 17(24), 21497–21508 (2009)ADS

El-Nabulsi, R.A., Golmankhaneh, A.K.: On fractional and fractal Einstein’s field equations. Mod. Phys. Lett. A 36(05), 2150030 (2021)ADSMathSciNetMATH

Friedrich, H.: On the regular and the asymptotic characteristic initial value problem for Einstein’s vacuum field equations. Proc. R. Soc. Lond. A Math. Phys. Sci. 375(1761), 169–184 (1981)ADSMathSciNetMATH

Friedrich, H.: On the hyperbolicity of Einstein’s and other gauge field equations. Commun. Math. Phys. 100(4), 525–543 (1985)ADSMathSciNetMATH

Friedrich, H.: On the existence of n-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure. Commun. Math. Phys. 107(4), 587–609 (1986)ADSMathSciNetMATH

Friedrich, H., Nagy, G.: The initial boundary value problem for Einstein’s vacuum field equation. Commun. Math. Phys. 201(3), 619–655 (1999)ADSMathSciNetMATH

Godel, K.: An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Rev. Mod. Phys. 21(3), 735–744 (1949)MathSciNetMATH

Guilfoyle, B.S.: Interior Weyl-type solutions to the Einstein–Maxwell field equations. Gen. Relativ. Gravit. 31(11), 1645–1673 (1999)ADSMathSciNetMATH

Guo, J.-L., Yang, Z.-J., Song, L.-M., Pang, Z.-G.: Propagation dynamics of tripole breathers in nonlocal nonlinear media. Nonlinear Dyn. 101, 1147–1157 (2020)

Gupta, R.K., Jain, R., Kumar, S., Jyoti, D.: On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution. Pramana 95(3), 1–4 (2021)

Heinicke, C., Hehl, F.W.: Schwarzschild and Kerr solutions of Einstein’s field equation. Int. J. Mod. Phys. D 24(02), 1530006 (2015)ADSMathSciNetMATH

Jyoti, D., Kumar, S.: Exact non-static solutions of Einstein vacuum field equations. Chin. J. Phys. 68, 735–744 (2020)MathSciNet

Kaur, L., Wazwaz, A.M.: Einstein’s vacuum field equation: Painlevé analysis and Lie symmetries. Waves in Rand. Complex Media 31(2), 199–206 (2021)ADS

Khan, M.H., Wazwaz, A.M.: Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the \((2+ 1)\)-D Calogero–Bogoyavlenskii–Schiff equation. Heliyon 6(4), 03701 (2020)

Khater, A.H., Helal, M.A., Seadawy, A.R.: General soliton solutions of n-dimensional nonlinear Schrödinger equation. IL Nuovo Cimento 115B, 1303–1312 (2000)ADS

Liu, Y., Li, B., Wazwaz, A.M.: Novel high-order breathers and rogue waves in the Boussinesq equation via determinants. Int. J. Mod. Phys. B 43(6), 3701–3715 (2020)MathSciNetMATH

Lu, X., Chen, S.J.: Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dyn. 103(1), 947–977 (2021)MathSciNet

Ma, Y.L.: N-solitons, breathers and rogue waves for a generalized Boussinesq equation. Int. J. Comput. Math. 97(8), 1648–1661 (2020)MathSciNetMATH

Manjunatha, H.M., Narasimhamurthy, S.K., Nekouee, Z.: Static conformal elastic solution of Einstein’s field equations, arXiv preprint arXiv:2107.06648 (2021)

Moraes, P.H.R.S.: The trace of the trace of the energy-momentum tensor-dependent Einstein’s field equations. Eur. Phys. J. C 79(8), 1–5 (2019)

Rizvi, S.T., Seadawy, A.R., Mustafa, B., Ali, K., Ashraf, R.: Propagation of chirped periodic and solitary waves for the coupled nonlinear Schrödinger equation in two core optical fibers with parabolic law with weak non-local nonlinearity. Opt. Quantum Electron. 54, 545 (2022)

Rutz, S.F.: A Finsler generalisation of Einstein’s vacuum field equations. Gen. Relativ. Gravit. 25(11), 1139–1158 (1993)ADSMathSciNetMATH

Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos, Solitons Fractals 144, 110669 (2021)MathSciNet

Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation. Phys. Scr. 96(4), 045202 (2021)ADS

Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Phys. 19(1), 1–10 (2021)

Seadawy, A.R., Rizvi, S.T., Ali, I., Younis, M., Ali, K., Makhlouf, M.M., Althobaiti, A.: Conservation laws, optical molecules, modulation instability and Painlevé analysis for the Chen–Lee–Liu model. Opt. Quant. Electron. 53(4), 1–15 (2021)

Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Weierstrass, elliptic, Jacobi: bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation. Chaos, Solitons Fractals 160, 112258 (2022)MATH

Shah, K., Seadawy, A.R., Arfan, M.: Evaluation of one dimensional fuzzy fractional partial differential equations. Alex. Eng. J. 59, 3347–3353 (2020)

Shen, S., Yang, Z.-J., Li, X.-L., Zhang, S.: Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media. Commun. Nonlinear Sci. Numer. Simul. 103, 106005 (2021)MathSciNetMATH

Shen, S., Yang, Z.-J., Pang, Z.-G., Ge, Y.-R.: The complex-valued astigmatic cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. Appl. Math. Lett. 125, 107755 (2022)MATH

Singh, S., Sakkaravarthi, K., Murugesan, K., Sakthivel, R.: Benjamin-Ono equation: rogue waves, generalized breathers, soliton bending, fission, and fusion. Eur. Phys. J. Plus 135(10), 1–17 (2020)

Song, L.-M., Yang, Z.-J., Li, X.-L., Zhang, S.-M.: Coherent superposition propagation of Laguerre–Gaussian and Hermite–Gaussian solitons. Appl. Math. Lett. 102, 106114 (2020)MathSciNetMATH

Tolman, R.C.: Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev. 55(4), 364 (1939)ADSMATH

Ullah, M.S., Roshid, H.O., Ma, W.X., Ali, M.Z., Rahman, Z.: Interaction phenomena among lump, periodic and kink wave solutions to a \((3+ 1)\)-dimensional Sharma–Tasso–Olver-like equation. Chin. J. Phys. 68, 699–711 (2020)MathSciNet

Yang, Z.-J., Zhang, S.-M., Li, X.-L., Pang, Z.-G., Hong-Xia, B.: High-order revivable complex-valued hyperbolic-sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality. Nonlinear Dyn. 94, 2563–2573 (2018)

Younas, U., Younis, M., Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S., Sayed, S.: Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative. Results Phys. 20, 103766 (2021)

Titel: Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions
verfasst von: Syed T. R. Rizvi
Aly R. Seadawy
Sarfaraz Ahmed
Kashif Ali
Publikationsdatum: 01.02.2023
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 2/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-022-04451-8

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