Results in Physics, 2016 The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation.
Chen Yue, Aly Seadawy, Dianchen Lu
doaj
On the Cauchy problem for higher-order nonlinear dispersive equations [PDF]
arXiv, 2007 We study a class of higher-order KdV equations. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when in H^s(\R), for any real s.
arxiv
R-matrix for a geodesic flow associated with a new integrable peakon equation
, 2016 We use the r-matrix formulation to show the integrability of geodesic flow on an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$.
Holm, Darryl D., Qiao, Zhijun
core
Dispersive Hydrodynamics of Soliton Condensates for the Korteweg-de Vries Equation. [PDF]
J Nonlinear Sci, 2023 Congy T, El GA, Roberti G, Tovbis A.
europepmc +1 more source
A Sharp Bilinear Estimate for the Bourgain-type Space with Application to the Benjamin Equation [PDF]
arXiv, 2009 This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation.
arxiv
Exact solution of generalized inviscid Burgers' equation [PDF]
arXiv, 2009 Let $f,g:{\Bbb R}\to{\Bbb R}$ be integrable functions, $f$ nowhere zero, and $\phi (u)=\int du/f(u)$ be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers' equation $u_t+g(u).u_x=f(u)$ is given, by quadratures.
arxiv
A Refined Well-Posedness Result for the Modified KdV Equation in the Fourier-Lebesgue Spaces. [PDF]
J Dyn Differ Equ, 2023 Chapouto A.
europepmc +1 more source
Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables [PDF]
arXiv, 2009 We consider the KdV equation on the Sobolev space of periodic distributions. We obtain estimates of the solution of the KdV in terms of action variables.
arxiv
Superconformal Algebras and Supersymmetric Integrable Flows [PDF]
arXiv, 2009 This paper has been withdrawn by the authors. Because of a misunderstanding, the paper was submitted prematurely to the arXiv. A replacement will follow.
arxiv
The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy [PDF]
arXiv, 2012 In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
arxiv