Results 1 to 10 of about 340,065 (284)

Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method [PDF]

Scientific Reports
This research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-
Akhtar Hussain, Tarek F. Ibrahim, Fathea M. Osman Birkea, M. Sh. Yahya, Abaker A. Hassaballa, Herbert Mukalazi   +5 more
doaj   +2 more sources

Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials

Journal of Physics A: Mathematical and Theoretical, 2008
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of power-law and ...
Abramowitz M, Bernard Silvestre-Brac, Brau F, Brau F, Brau F, Claude Semay, Dirac P A M, Fabien Buisseret, Flügge S, Hall R L, Silvestre-Brac B, Silvestre-Brac B, Silvestre-Brac B   +12 more
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Extended Auxiliary Equation Method and Its Applications to Three Generalized NLS Equations [PDF]

Abstract and Applied Analysis, 2014
The auxiliary equation method proposed by Sirendaoreji is extended to construct new types of elliptic function solutions of nonlinear evolution equations.
Gui-qiong Xu
doaj   +4 more sources

Exact Solutions to Fractional Schrödinger–Hirota Equation Using Auxiliary Equation Method

Axioms
In this paper, we consider the fractional Schrödinger–Hirota (FSH) equation in the sense of a conformable fractional derivative. Through a traveling wave transformation, we change the FSH equation to an ordinary differential equation.
Guangyuan Tian, Xianji Meng
doaj   +2 more sources

Bifurcation, chaotic behavior, sensitivity analysis, and dynamical investigations of third-order Schrödinger equation using new auxiliary equation method [PDF]

Scientific Reports
This current study presents a precise analytical examination of the generalized third-order nonlinear Schrödinger equation through the application of the new auxiliary equation method.
Mehreen Fatima, Muhammad Abbas, Yagoub. A. S. Arko, Tahir Nazir, Asnake Birhanu, Muhammad Zain Yousaf   +5 more
doaj   +2 more sources

Traveling wave solutions for space-time fractional Cahn Hilliard equation and space-time fractional symmetric regularized long-wave equation

Alexandria Engineering Journal, 2021
Over the last few years, a direct method known as the new auxiliary method has been shown to solve non-linear partial differential equations effectively where this method can give more exact solutions compared to the traditional direct methods.
Muhammad Asim Khan, M. Ali Akbar, Nur Nadiah binti Abd Hamid   +2 more
doaj   +1 more source

Exploration of solitary wave solutions of highly nonlinear KDV–KP equation arise in water wave and stability analysis

Results in Physics, 2023
For intellectual curiosity, in this manuscript, we study the sixth-order highly nonlinear generalized Korteweg–de Vries–Kadomtsev–Petviashvili dynamical model.
Sonia Akram, Jamshad Ahmad, Shafqat-Ur- Rehman, Shalan Alkarni, Nehad Ali Shah   +4 more
doaj   +1 more source

Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation

Mathematics, 2022
In this paper, we study a generalized scale-invariant analogue of the well-known Korteweg–de Vries (KdV) equation. This generalized equation can be thought of as a bridge between the KdV equation and the SIdV equation that was discovered recently, and ...
Lewa’ Alzaleq, Valipuram Manoranjan, Baha Alzalg   +2 more
doaj   +1 more source

A Reliable Treatment for Nonlinear Differential Equations

Journal of Mathematics, 2021
In this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopy parameter method (ALHPM).
H. R. Marasi, M. Sedighi, H. Aydi, Y. U. Gaba   +3 more
doaj   +1 more source

Exact wave solutions of the nonlinear Rosenau equation using an analytical method

Open Physics, 2021
The purpose of the current study is to find exact travelling wave solutions of the Rosenau equation. By the use of the extended auxiliary equation method, various exact solutions are obtained in terms of Jacobi elliptic functions and exponential ...
Alotaibi Trad, Althobaiti Ali
doaj   +1 more source