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New plenteous soliton solutions and other form solutions for a generalized dispersive long-wave system employing two methodological approaches

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Abstract

In this research, we concentrated on the dispersive long wave system in two horizontal directions for dispersive nonlinear waves on the shallow water of an open sea or a wide channel of finite depth. We investigated this governing system by using two different methodologies, namely the generalized exponential rational function (GERF) method, and the new modified generalized exponential rational function (MGERF) method. The GERF method was first introduced by Ghanbari and Inc (Eur. Phys. J. Plus 133:-142, 2018) for finding the soliton solutions for highly nonlinear partial differential equations (NLPDEs). This technique is very reliable and straightforward and reduces the NLPDEs into ordinary differential equations (ODEs) under the wave transformation. Being motivated by the GERF technique, we proposed a newly modified generalized exponential rational function (MGERF) method under wave transformation. We obtained a diverse set of solutions involving trigonometric forms, hyperbolic forms, rational forms, and so on, which have a broad application spectrum in fields such as plasma physics, nonlinear optics, optical fibers, and nonlinear sciences by utilizing these methods. Due to the presence of various arbitrarily chosen constants, these solutions exhibit extensive and rich dynamical behavior. Based on the dynamical behaviors, we discovered that the soliton solutions were collisions of solitons, breather-like solitons, line-form solitons, multi-solitons, solitary waves, lump-form solitons, and other forms. Consider a nonlinear system with dispersive and dispersion terms, a nonlinear Schrödinger equation, and fractional nonlinear evolution equations, which will yield additional interesting and more achievable results. Finding solutions to these equations in solitary wave solution forms will be a difficult task.

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Acknowledgements

The authors would like to express their appreciation to the Editor and the referees for their insightful and informative comments. The author, Sachin Kumar, would also like to thank the Institution of Eminence, University of Delhi, for financial support provided through the Faculty Research Programme Grant-IoE via (Ref. No./IoE/2021/12/FRP).

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  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Monika Niwas & Sachin Kumar

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  1. Monika Niwas
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Niwas, M., Kumar, S. New plenteous soliton solutions and other form solutions for a generalized dispersive long-wave system employing two methodological approaches. Opt Quant Electron 55, 630 (2023). https://doi.org/10.1007/s11082-023-04847-0

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