Results 51 to 60 of about 274 (149)

Surface Wave Solutions in 1D and 2D for the Broer–Kaup–Boussinesq–Kupershmidt System

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT The Broer–Kaup–Boussinesq–Kupershmidt (BKBK) system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification introduces backward diffusion terms proportional to a real parameter κ$\kappa$.
Darryl D. Holm, Ruiao Hu, Hanchun Wang
wiley   +1 more source

Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
wiley   +1 more source

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Mathematics
The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity
Natanael Karjanto
doaj   +1 more source

Local Well‐Posedness for the Fourth‐Order Schrödinger Equation With Quadratic Derivative Nonlinearities in Fourier–Lebesgue Spaces

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
We investigate the Cauchy problem for the fourth‐order Schrödinger equation with quadratic nonlinearities involving second‐order derivatives: uxxu, uxxū, (ux)2, uūxx, and |ux|2, where u = u(x, t) is a complex‐valued function defined on R×R. The flow map of this Cauchy problem with the nonlinear terms uxxu or uxxū fails to be C2 differentiable at zero ...
Long Xiao, Ting Chen, Xian-Ming Gu
wiley   +1 more source

The Nonlinear Schrödinger Equation Derived From the Fifth-Order Korteweg–de Vries Equation Using Multiple Scales Method

International Journal of Differential Equations
The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems.
Murat Koparan
doaj   +1 more source

Rogue waves and downshifting in the presence of damping [PDF]

Natural Hazards and Earth System Sciences, 2011
Recently Gramstad and Trulsen derived a new higher order nonlinear Schrödinger (HONLS) equation which is Hamiltonian (Gramstad and Trulsen, 2011). We investigate the effects of dissipation on the development of rogue waves and downshifting by adding an ...
A. Islas, C. M. Schober
doaj   +1 more source

Optical Solitons and Analysis of Chaotic Nature for the Temporal M‐Fractional Yajima–Oikawa Model in Shortwave and Longwave

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study proposes a comprehensive study on fractional soliton solutions and chaotic nature for the temporal M‐fractional Yajima–Oikawa (YO) model in shortwave and longwave regimes. Utilizing the new Jacobian elliptic function method, the optical soliton solutions are examined with diverse categories, including kinky‐periodic wave, kink with bell wave,
Md. Mamunur Roshid, Mrityunjoy Kumar Pandit, Mahtab Uddin, Golam Mostafa, Harun-Or-Roshid, Pramita Mishra   +5 more
wiley   +1 more source

Fractional isospectral and non-isospectral AKNS hierarchies and their analytic methods for N-fractal solutions with Mittag-Leffler functions

Advances in Difference Equations, 2021
Ablowitz–Kaup–Newell–Segur (AKNS) linear spectral problem gives birth to many important nonlinear mathematical physics equations including nonlocal ones.
Bo Xu, Yufeng Zhang, Sheng Zhang
doaj   +1 more source

Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 12, Page 2305-2353, December 2025.
Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
wiley   +1 more source

Rogue waves and periodic solutions of a nonlocal nonlinear Schrödinger model

Physical Review Research, 2020
In the present paper, a nonlocal nonlinear Schrödinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations by considering them as fixed points in space-time.
C. B. Ward, P. G. Kevrekidis, T. P. Horikis, D. J. Frantzeskakis   +3 more
doaj   +1 more source