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New analytic wave solutions to (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation using the modified extended map** method
In this study, the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBME) is examined. KP-BBM is used as a water wave...
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Lie group analysis, optimal system and analytic solutions of a (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation for the fluid flow around an offshore structure
Offshore structures are used in the maritime engineering, oil industry, gas industry, energy-harvesting systems, transportation and aquaculture. In...
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New traveling wave solutions for paraxial wave equation via two integrating techniques
The purpose of the presented work is to obtain the exact solutions of the Paraxial wave equation using two different methods, the modified auxiliary...
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M-lump, interaction between lumps and stripe solitons solutions to the (2+1)-dimensional KP-BBM equation
In this paper, we have earned the M-lump solutions, the interaction within stripe solitons and lumps which are more considered mentioning that lumps...
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Unique soliton solutions to the nonlinear Schrödinger equation with weak non-locality and cubic–quintic–septic nonlinearity in nonlinear optical fibers
In this article, we will introduce new types of private soliton solutions to the higher order nonlinear Schrödinger equation (HOSE), containing...
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Extraction of newly soliton wave structure to the nonlinear damped Korteweg–de Vries dynamical equation through a computational technique
The damped Korteweg-de Vries (D-KdV) equation is a significant extension of the Korteweg–de Vries equation, which plays an important role in...
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Travelling-wave, Mixed-lump-kink and Mixed-rogue-wave-kink Solutions for an Extended (3+1)-dimensional Shallow Water Wave Equation in Oceanography and Atmospheric Science
Shallow water waves are seen in oceanography, atmospheric science, and other fields. In this paper, we investigate an extended (3+1)-dimensional...
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New exact solutions of the (3+1)-dimensional double sine-Gordon equation by two analytical methods
The (3+1)-dimensional double sine-Gordon equation plays a crucial role in various physical phenomena, including nonlinear wave propagation, field...
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Wave structures of the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation: analytical insights utilizing two high impact methods
In this manuscript, we employ the unified method and the Sardar subequation method to systematically analyze various wave structures within the...
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Dynamical behavior of the fractional coupled Konopelchenko–Dubrovsky and (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznestsov equations
This work studies soliton solutions of time-fractional coupled Konopelchenko–Dubrovsky (CKDE) and (3 + 1)-dimensional modified Korteweg–de...
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Homoclinic and N-soliton solutions to variable-coefficient KP equation arising two-temperature ions in dusty plasma
In this article, a variable-coefficient Kadomtsev–Petviashvili (VCKP) equation is studied by using the Hirota technique. The formulae of the bilinear...
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Investigating the irrotational gravity waves along the surface of an inviscid incompressible fluid model by modified nonlinear Schrödinger equation
This article discusses the solitons as well as additional solutions to the modified nonlinear Schrödinger equation, which appears in the study of...
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Jacobi elliptic solutions, bright, compound bright-complex singular solitons of \(\left( 3+1\right) -\) dimensional Wazwaz Kaur Boussinesq equation
In this research communication, the (3 + 1)-dimensional Wazwaz Kaur Boussinesq equation is studied and solved by the direct algebraic method, namely...
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A variety of optical wave solutions to space–time fractional perturbed Kundu–Eckhaus model with full non-linearity
In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu–Eckhaus model with full non-linearity are obtained by...
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Multi wave, kink, breather, Peregrine-like rational and interaction solutions for the concatenation model
Under investigation is a concatenation model having Kerr law of nonlinearity. This model encompasses nonlinear Schrödinger’s equation,...
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A study on single-iteration sobolev descent for linear initial value problems
Mahavier and Montgomery construct a Sobolev space for approximate solution of linear initial value problems in a finite difference setting in...
