Dynamical Behavior of the Solutions of Coupled Boussinesq–Burgers Equations Occurring at the Seaside Beaches

Kumar, Raj; Pandey, Kripa Shankar; Kumar, Avneesh

doi:10.1007/s13538-022-01195-4

Cited by 8 publications

(3 citation statements)

References 38 publications

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“…There are numerous intricate natural phenomena in our lives and surroundings that have many implications. Such phenomena are often described by nonlinear evolution equations (NLEEs), which occur in fields such as fluid mechanics [1], genetic theories [2], condensed materials science [3], marine science [4], optical and computational physics [5], plasma physics [6,7], chaotic sciences [8] and other fields [9]. The significance of NLEEs attracted the research community due to their distinctive properties.…”

Section: Introduction 1aims and Scopementioning

confidence: 99%

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

Kumar,

Pandey,

Yadav

et al. 2024

Phys. Scr.

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The goal of this study is to get analytical solutions to the Bogoyavlensky-Konopelchenko equation, which describes an interaction of a long-wavelength wave moving along the x-axis and a Riemann wave-form moving along the y-axis. The equation has been widely used in soliton theory, fluid dynamics, optics, biological systems, and differential geometry. It is a member of the Ablowitz-Kaup-Newell-Segur hierarchy of integrable systems. By exploiting the classical Lie symmetry approach, the equation is reduced to an ordinary differential equation. After solving the second similarity reduction, the authors derived a novel class of solutions for each case. Additionally, the derived solutions comprise some parameters, and various functions might be utilized to explore wave profiles like stationary, dark, and bright soliton, parabolic dark and bright soliton, and progressive nature. Solutions are compared with previous researches [18-25] to show novelty of results. Solutions can help with numerous applications in physics, such as fluid dynamics, plasma physics, and nonlinear optics.

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Section: Introduction 1aims and Scopementioning

confidence: 99%

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

Kumar,

Pandey,

Yadav

et al. 2024

Phys. Scr.

Self Cite

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“…Therefore, the Lie group is used in a variety of contexts, including the construction of explicit solutions to PDEs. The physical significance and theoretical analysis of the proposed method have been investigated in the existing literature [17,18,[39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

A study on analytical solutions and conservation laws of the cgKP occurring in straits

Shukla,

Kumar,

Kumar

2023

Phys. Scr.

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The (2+1)-KP equation in its canonical generalized form i.e. cgKP relates to water waves that propagate exclusively in straits or rivers, as opposed to unbounded surfaces such as oceans. The cgKP, an example of a complex nonlinear system, is solved analytically in this article. To solve analytically the cgKP, the Lie symmetries are generated to get several novel invariant solutions to the cgKP, which are rare as far as the authors are aware. The cgKP reduces to an equivalent PDE with fewer independent variables than the original PDE. Animation profiles are utilized to better understand the obtained solutions, and they reflect transition from doubly solitons to single soliton; transition from negatons to positons and negatons; single solitons and multi solitons; annihilation of multi solitons; elastic parabolic profiles; single front parabolic and positons; multi-negatons on flat surface, and fusion of multi solitons wave types. Because of the presence of arbitrary functions in infinitesimal transformations, the Lie symmetry method has the potential to provide more variety in solutions. When compared to previously published findings, this study convincingly highlights the originality of the solutions. In the future, without assuming any relation among the arbitrary functions involved in infinitesimals, someone can explore the possibility of some more solutions. The physical character of the analytical results could help coastal engineers develop models of coastlines and ports in the current study.

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“…Wu and Zhang [22] derived the (1 + 1)dimensional classical Boussinesq equation, which is used to simulate nonlinear dispersive long gravity waves propagating along two horizontal directions in shallow water of a uniform depth. In recent years, many scholars have studied the equation [23][24][25]. In the third part, we calculate the self-adjoint properties and their conservation laws [26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties

Zhou,

Ju,

Zhao

et al. 2023

Symmetry

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In this paper, we consider how to find new exact solutions for nonlinear partial differential equations using the extended Kudryashov method. This method mainly uses the Riccati equation and the Bernoulli equation where there are some underdetermined constant parameters. And we also use the concept of symmetry to study its reduction equation, Lie transformation group, self-adjointness, and conservation laws. This paper mainly studies the Boussinesq class and the shallow water wave equation in (1 + 1) dimensions and tries to find new exact solutions and symmetry properties of them.

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Dynamical Behavior of the Solutions of Coupled Boussinesq–Burgers Equations Occurring at the Seaside Beaches

Cited by 8 publications

References 38 publications

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

A study on analytical solutions and conservation laws of the cgKP occurring in straits

Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties

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