Results 41 to 50 of about 23,327 (208)

Modulation of Camassa--Holm equation and reciprocal transformations [PDF]

, 2005
We derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure.
Abenda, Simonetta, Grava, Tamara
core   +2 more sources

An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion

, 2001
We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves integrability ...
A. S. Fokas, A. S. Fokas, A. S. Fokas, A. S. Fokas, B. Fuchssteiner, D. D. Holm, D. D. Holm, Darryl D. Holm, G. B. Whitham, G. Misiolek, Georg A. Gottwald, Holger R. Dullin, I. M. Gelfand, J. E. Marsden, Li Zhi, M. Alber, M. Alber, M. J. Ablowitz, P. D. Weidman, P. J. Olver, R. Beals, R. Camassa, Y. Kodama, Y. Kodama, Y. Kodama, Y. Kodama   +25 more
core   +1 more source

Conformal Properties and Baecklund Transform for the Associated Camassa-Holm Equation [PDF]

, 2005
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation.
Beals, Beals, Bol, Camassa, Constantin, Constantin, Constantin, Constantin, Constantin, Constantin, Constantin, Depireux, Dickey, Dorfman, Fisher, Fokas, Fokas, Galas, Gieres, Hille, Hone, Hone, Johnson, Johnson, Lenells, Lou, Matveev, Matveev, Matveev, Matveev, Matveev, Misiolek, Nucci, Rasinariu, Rossen Ivanov, Schiff, Schiff, Shabat, Weiss, Weiss, Wilson   +40 more
core   +4 more sources

A polynomial conjecture connected with rogue waves in the KdV equation

Partial Differential Equations in Applied Mathematics, 2021
A polynomial conjecture, associated with rational solutions including rogue wave solutions of the KdV equation, is presented. The conjecture can be used to show that for the bilinear KdV equation, an arbitrary linear combination of two Wronskian ...
Wen-Xiu Ma
doaj   +1 more source

2 + 1 KdV(N) equations [PDF]

Journal of Mathematical Physics, 2011
We present some nonlinear partial differential equations in 2 + 1-dimensions derived from the KdV equation and its symmetries. We show that all these equations have the same 3-soliton solution structures. The only difference in these solutions are the dispersion relations. We also show that they possess the Painlevé property.
Gurses, M., Pekcan, A.
openaire   +6 more sources

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

Robot‐Assisted Reconstruction and Control of the Pechmann Reaction Network

Angewandte Chemie, Volume 138, Issue 6, 2 February 2026.
Using an in‐house built robotic platform, we systematically explored the classic Pechmann reaction across a wide range of reaction conditions, uncovering a rich and previously unexplored network of reactivity. This approach led to the discovery of 11 novel products, including rare benzofurans formed through non‐classical pathways.
Bibek Prajapati, Wai‐Shing Wong, Rafał Frydrych, Diana V. Kolygina, Yankai Jia, Benito Marazzi, Nikolaos Vagkidis, Peter R. Schreiner, Bartosz A. Grzybowski   +8 more
wiley   +2 more sources

Fredholm Determinant and Wronskian Representations of the Solutions to the Schrödinger Equation with a KdV-Potential

Axioms
From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants.
Pierre Gaillard
doaj   +1 more source

Explicit solutions of the fifth-order KdV type nonlinear evolution equation using the system technique

Results in Physics, 2016
We consider the generalized fifth-order KdV type nonlinear evolution equation with variable coefficients. The system technique has been applied rigorously in order to find new exact solutions of the considered equations.
Hyunsoo Kim, Sunmi Lee
doaj   +1 more source

Loop Groups and Discrete KdV Equations

, 2002
A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al.
Bobenko A I, Boiti M, Drazin P G, Hetrich-Jeromin U, Hirota R, Hu X-B, Jeremy Schiff, Mukaihira A, Nijhoff F, Pressley A, Schiff J, Schiff J, Segal G, Wilson G, Wilson G   +14 more
core   +2 more sources