A study of multi-soliton solutions, breather, lumps, and their interactions for kadomtsev-petviashvili equation with variable time coeffcient using hirota method

Abstract

This paper investigates the new KP equation with variable coefficients of time ‘t’, broadly used to elucidate shallow water waves that arise in plasma physics, marine engineering, ocean physics, nonlinear sciences, and fluid dynamics. In 2020, Wazwaz [1] proposed two extensive KP equations with time-variable coefficients to obtain several soliton solutions and used Painlevé test to verify their integrability. In light of the research described above, we chose one of the integrated KP equations with time-variable coefficients to obtain multiple solitons, rogue waves, breather waves, lumps, and their interaction solutions relating to the suitable choice of time-dependent coefficients. For this KP equation, the multiple solitons and rogue waves up to fourth-order solutions, breather waves, and lump waves along with their interactions are achieved by employing Hirota's method. By taking advantage of Wolfram Mathematica, the time-dependent variable coefficient's effect on the newly established solutions can be observed through the three-dimensional wave profiles, corresponding contour plots. Some newly formed mathematical results and evolutionary dynamical behaviors of wave-wave interactions are shown in this work. The obtained results are often more advantageous for the analysis of shallow water waves in marine engineering, fluid dynamics, and dusty plasma, nonlinear sciences, and this approach has opened up a new way to explain the dynamical structures and properties of complex physical models. This study examines to be applicable in its influence on a wide-ranging class of nonlinear KP equations.

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

“…Finding the exact solutions for NLEE is an essential task as NLEE describes numerous phenomenon in nonlinear dynamics, engineering, optical fibre, plasma physics, fluid mechanics, natural sciences, biomedical applications etc. A large number of researchers and mathematicians have developed various effective techniques for computing exact solutions of NLPDEs (nonlinear partial differential equations), for instance, tanh function method [1], Hirota's bilinear method [2,3], the Jacobi elliptic function expansion method [4], Kudryashov method [5], the G ′ G -expansion method [6], Darboux transformation method [7], the Backlund transformation method [8], the inverse scattering method [9], Lie-symmetry analysis [10], multiple exp-function method, and many others. Among these techniques, GERF method [11][12][13][14] is very effective, robust and straightforward approach for finding the abundant exact soliton-form solutions of various NLPDEs.…”

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

“…Also, the exact solutions of these equations are crucial to studying the propagation of Rossby waves [8][9][10][11]. So, many methods have been proposed on how to solve the exact solutions to nonlinear equations, for instance, the Hirota method [12][13][14], the Jacobi elliptic function expansion method [15][16][17][18], the G′/G-expansion method [19][20][21][22][23], the Exp (− Φ(ξ))-expansion method [24,25], the generalised exponential rational function method [26][27][28], the negative power expansion method [29], the hyperbolic function expansion method [30][31][32][33], the extended sub-equation method [34], (ω/g)-expansion method [35], the improved sub-ODE method [36], the Riccati-Bernoulli sub-ODE method [37][38][39][40], the Lie symmetry technique [41][42][43][44][45][46][47], the fractional sub-equation [48] etc. Tese are valid methods and tools for computing nonlinear equations.…”

Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed

“…A constant-coefficient equation and a time-dependent-coefficient equation were developed first, the Painlevé integrability were confirmed next, and multiple real and multiple complex soliton solutions were obtained by complex forms of Hirota's method finally. Further, Kumar and Mohan in [36] gave many types of solutions and figures of KP equation developed in [33] by using the Hirota bilinear method. Currently, none of the research involves the HSI equation (3) with variable coefficients.…”