Results 71 to 80 of about 3,238 (183)

Coupled Ablowitz-Ladik equations with branched dispersion

, 2017
Complete integrability and multisoliton solutions are discussed for a multicomponent Ablowitz-Ladik system with branched dispersion relation. It is also shown that starting from a "diagonal" (in two-dimensions) completely integrable Ablowitz-Ladik ...
Babalic, Corina N., Carstea, A. S.
core   +1 more source

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.
This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
wiley   +1 more source

Retrieval of the optical soliton solutions of the perturbed Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity having the spatio‐temporal dispersion

Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2164-2178, 30 January 2025.
In this study, we obtained optical soliton solutions of the perturbed nonlinear Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity in the presence of spatio‐temporal dispersion. This equation models the propagation of optical pulses in fiber optic cables.
Ismail Onder, Aydin Secer, Muslum Ozisik, Mustafa Bayram   +3 more
wiley   +1 more source

Q-soliton solution for two-dimensional q-Toda lattice

Қарағанды университетінің хабаршысы. Физика сериясы, 2019
The Toda lattice is a non-linear evolution equation describing an infinite system of masses on a line that interacts through an exponential force. The paper analyzes the construction of soliton solution for the q-Toda lattice in the two-dimensional case.
Б.Б. Кутум, Г.Н. Шайхова
doaj   +1 more source

A class of lump solutions and localized excitations for the generalized (3 + 1)-dimensional KP equation

Results in Physics, 2020
Based on symbolic computation and Hirota bilinear form, a class of lump solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation is given. As a result, the lump solution shows a new perspective to knowledge them. Meanwhile,
Ping Cui
doaj   +1 more source

Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

, 1997
Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered.
B. G. Konopelchenko, L. V. Bogdanov, Nizhnik L. P., Sato M., Ueno K., Veselov A. P., Zakharov V. E., Zakharov V. E.   +7 more
core   +1 more source

Advanced Mathematical Approaches for the Kadomtsev–Petviashvili and Bogoyavlensky–Konopelchenko Equations in Applied Sciences

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
The Kadomtsev–Petviashvili (KP) equation and the Bogoyavlensky–Konopelchenko (BK) equation are fundamental models in the study of nonlinear wave dynamics, describing the evolution of weakly dispersive, quasi‐two‐dimensional (2D) wave phenomena in integrable systems.
Md. Abdul Aziz, Jingli Ren
wiley   +1 more source

Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation

Mathematics, 2020
In this paper, we investigate the (2 + 1)-dimensional Hirota–Satsuma–Ito (HSI) shallow water wave model. By introducing a small perturbation parameter ϵ, an extended (2 + 1)-dimensional HSI equation is derived.
Yuefeng Zhou, Chuanjian Wang, Xiaoxue Zhang   +2 more
doaj   +1 more source

Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

, 2007
We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe
A. Baha Balantekin, A. Klümper, A. Kuniba, A. V. Zabrodin, A. V. Zabrodin, A. V. Zabrodin, A. Zabrodin, E. Date, I. Bars, I. Krichever, I. Macdonald, L. A. Takhtadzhan, L. Faddeev, N. M. Bogoliubov, N. Shinzawa, N. Shinzawa, P. Kulish, P. P. Kulish, P. P. Kulish, R. Hirota, S. Saito, V. Bazhanov, V. Kac, Z. Tsuboi   +23 more
core   +2 more sources

On the Study of Nonlinear Murray Equation in Non‐Newtonian Fluids: Fractional Solitary Wave Structures, Chaos, and Sensitivity Demonstration

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This article introduces fractional solitary wave structures to the nonlinear Murray equation by applying advanced techniques, namely the generalized Arnous method and the modified generalized Riccati equation mapping method (MGREMM). This equation is known as a generalization of the nonlinear reaction–diffusion equation, which describes the diffusion ...
J. Muhammad, U. Younas, Haroon, H. Mukalazi, M. E. Meligy, K. A. Alnowibet, Shikha Binwal   +6 more
wiley   +1 more source