Results 81 to 90 of about 18,365 (215)

The Generalized Harry Dym Equation

, 2003
The Harry Dym equation is generalized to the system of equations in the manner as the Korteweg - de Vries equation is generalized to the Hirota - Satsuma equation . The Lax and Hamiltonian formulation for this generalization is given.This generalized Lax
Adler, Alber, Antonowicz, Brunelli, Brunelli, Błaszak, Dodd, Gelfand, Hirota, Konopelchenko, Manna, Ziemowit Popowicz   +11 more
core   +1 more source

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation

Mathematics
In this paper, we prove that the isospectral flows associated with both the x-part and the n-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation.
Junwei Cheng, Xiang Tian
doaj   +1 more source

Near-linear dynamics in KdV with periodic boundary conditions

, 2009
Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data.
Colliander J Keel M Staffilani G Takaoka H Tao T, Kapeller T, Kuksin S, M B Erdoğan, N Tzirakis, Temam R, V Zharnitsky   +6 more
core   +2 more sources

Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor, Xianhua Song, Muhammad Shakeel, Muhammad Qamar Fareed, Baboucarr Ceesay, Kang-Jia Wang   +5 more
wiley   +1 more source

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source

On the origin of the Korteweg-de Vries equation

, 2011
The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves.
de Jager, E. M.
core  

The fifth‐order Korteweg‐de Vries equation [PDF]

International Journal of Mathematics and Mathematical Sciences, 1996
Decomposition is applied to the 5th‐order KdV equation.
openaire   +3 more sources

Cuckoo Search Optimized Fractional Physics‐Informed Neural Networks for Fourth‐Order Time‐Fractional Partial Differential Equations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Time‐fractional fourth‐order partial differential equations (PDEs) are typically important in the modeling of complex physical systems that have long‐memory effects and high‐order transverse spatial interaction. The paper presents a new hybrid method, called the Cuckoo Search–optimized fractional physics‐informed neural network (fPINN‐CS), that, to the
Ali Alkhathlan, Faris Kateb, Tauqeer Ahmad, Muhammad Sulaiman, Mohammed Abdullah Salman, Smritijit Sen   +5 more
wiley   +1 more source

On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

, 2008
We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint.Comment:
Baranetskii V B, Belokolos E D, Bikbaev R F, Bikbaev R F, Bondareva I, Bondareva I N, Boutet de Monvel A, Buslaev V S, Eckhaus W, Egorova I Teschl G, Ermakova V D, Ermakova V D, Faddeev L D, Firsova N E, Firsova N E, Gerald Teschl, Gesztesy F, Gesztesy F Ratnaseelan R Teschl G Gohberg I, Iryna Egorova, Its A R, Kamvissis S Teschl G, Kamvissis S Teschl G, Katrin Grunert, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Krüger H Teschl G, Kuznetsov E A, Lax P D, Levitan B M, Marchenko V A, Novikov S P   +33 more
core   +2 more sources