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Novel Soliton Molecules, Periodic Wave and other Diverse Wave Solutions to the New (2 + 1)-Dimensional Shallow Water Wave Equation
In this research, we focus on some novel exact solutions of the new (2 + 1)-dimensional shallow water wave equation (SWWE). First, the soliton...
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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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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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The traveling wave solutions for generalized Benjamin–Bona–Mahony equation
The traveling wave solutions of generalized BBM equation with any power are investigated. The existence and numbers of bell solitary wave solutions,...
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Multi-wave complexiton, multi-wave, interaction-wave and the travelling wave solutions to the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for the incompressible fluid
The current research aims to look into the exact solutions (ESs) of the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation (BLMPE), which...
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Exploring soliton solutions and interesting wave-form patterns of the (1 + 1)-dimensional longitudinal wave equation in a magnetic-electro-elastic circular rod
In this work, we use two newly powerful and efficient techniques, the unified method and the unified Riccati equation expansion (UREE) method, to...
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Multiple solitons solutions, lump solutions and rogue wave solutions of the complex cubic Ginzburg–Landau equation with the Hirota bilinear method
In this paper, we obtain the exact solutions of the (1+1) dimensional complex cubic Ginzburg–Landau equation (CCGLE) by using the Hirota bilinear...
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Solitary wave, undular-bore and wave-maker solutions of the cubic, quartic and quintic nonlinear generalized equal width (GEW) wave equation
Solitary wave solutions of the generalized equal width (GEW) wave equation are existing in the literature but undular-bore and wave-maker solutions...
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Traveling Wave Solutions to Equations of Two-Velocity Deep Bed Filtration
AbstractTraveling wave solutions to the deep bed filtration system are constructed for a model with different velocities of a carrier fluid and...
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New Perceptions for the Soliton Solutions to the Complex Wave Patterns Model Against its Numerical Solutions
The main target of this article is extracting new various types of the solitons emerging from the complex wave patterns which is famous model arising...
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Exact solutions of cubic-quintic-septimal nonlinear Schrödinger wave equation
Nonlinear phenomena, characterized by behaviors that cannot be explained by linear systems and has significant challenges in understanding and...
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Multi wave solutions and wave propagation in plasma physics over the Gilson-Pickering equation by modified extended tanh-function method
In this paper, the Gilson-Pickering equation which enables a wave propagation in plasma physics and crystal lattice theory is studied. Based on the...
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The classification of exact travelling wave solutions to two-component Dullin–Gottwald–Holm system
In this study, by making use of the direct integral method and the complete discrimination system for the polynomial method, all the travelling wave...
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Resonant multiple soliton and rogue type multiple lump wave solutions of the modified KdV–KP equation
This study investigates the precise solutions of the (2+1)-dimensional modified KdV–KP equation. Resonant multiple soliton solutions are examined by...
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Modulational instability, optical solitons and travelling wave solutions to two nonlinear models in birefringent fibres with and without four-wave mixing terms
The paper aims to construct optical solitons and travelling wave solutions to two birefringent nonlinear models which consist of two-component form...
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The Functionally Invariant Solutions and Nonlinear Wave Equations
An overview of the application of the functionally invariant solutions method for the nonlinear wave equation is given. A generalization of this...
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New solitary wave solutions of space-time fractional dynamical models
In this article, new traveling wave solutions are retrieved for two space-time fractional models: the resonant nonlinear Schrödinger equation and the...
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Stability, modulation instability analysis and new travelling wave solutions of non-dissipative double-dispersive microstrain wave model within micro-structured solids
This manuscript offers an in-depth analysis of the behavior of non-dissipative double-dispersive microstrain waves within microstructured solids,...
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New exact solitary wave solutions of the generalized (3 + 1)-dimensional nonlinear wave equation in liquid with gas bubbles via extended auxiliary equation method
This article will investigate the exact solitary wave solutions of the (3 + 1) generalized nonlinear wave equation with gas bubbles. Gas...
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Traveling Wave Solutions to the One-Phase Muskat Problem: Existence and Stability
We study the Muskat problem for one fluid in an arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In...