Results 61 to 70 of about 403 (167)

Explicit Exact Solutions of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Evolution Equation Using the Reliable Methods

International Journal of Mathematics and Mathematical Sciences, 2020
In this article, we utilize the G′/G2-expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions.
Supaporn Kaewta, Sekson Sirisubtawee, Nattawut Khansai   +2 more
doaj   +1 more source

Exact Solutions and Nonlinear Dynamical Behavior in a Navier‐Stokes‐Type Model for Elastic Cylindrical Vessels: An Analytical and Computational Approach

Engineering Reports, Volume 8, Issue 6, June 2026.
This study investigates a nonlinear Navier‐Stokes‐type model for elastic cylindrical vessels. Exact solutions are derived via the Bäcklund transformation and the ϕ6$$ {\phi}^6 $$‐expansion method, and dynamical behaviors are analyzed using bifurcation and chaos tools, revealing diverse wave structures and parameter‐dependent propagation characteristics.
Sheikh Zain Majid, Fatma Nur Kaya Sağlam, Mohammad Safi Ullah   +2 more
wiley   +1 more source

Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

Journal of Applied Mathematics, 2014
The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper.
Shi Jing, Yan Xin-li
doaj   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

New Exact Solutions for a Higher Order Wave Equation of KdV Type Using Multiple G′/G-Expansion Methods

Advances in Mathematical Physics, 2014
The G′/G-expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV type equation of neglecting the highest ...
Yinghui He
doaj   +1 more source

Chebyshev Smoothing With Adaptive Block‐FSAI Preconditioners for the Multilevel Solution of Higher‐Order Problems With the Partition of Unity Method

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V‐cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind, for the efficient solution of linear systems arising from a conforming discretization of higher‐order partial differential ...
Pablo Jiménez Recio, Marc Alexander Schweitzer   +1 more
wiley   +1 more source

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

Results in Physics, 2018
In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its ...
Innocent Simbanefayi, Chaudry Masood Khalique   +1 more
doaj   +1 more source

On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2021
In this work, we consider (3+1) dimensional nonlinear partial differential equations, namely modified KdV and Benjamin-Bona-Mahony equations. Different types of solutions to these equations are derived by Jacobi elliptic sine function expansion method ...
Ömer Faruk Gözükızıl, Hami Gündoğdu   +1 more
doaj  

Optical solutions of the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using two different methods

Results in Physics, 2020
This paper studies the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation. The first integral of this equation, the phase portraits and the effective potentials are provided. Two different methods are applied to find exact analytical solutions.
Eric Tala-Tebue, Cedric Tetchoka-Manemo, Hadi Rezazadeh, Ahmet Bekir, Yu-Ming Chu   +4 more
doaj   +1 more source

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source