Results 71 to 80 of about 17,995 (145)
Stochastic Multisymplectic PDEs and Their Structure‐Preserving Numerical Methods
Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.ABSTRACT We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637].
Ruiao Hu, Linyu Peng
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A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation [PDF]
, 2010 Consider a one-dimensional Schroedinger operator which is a short range perturbation of a finite-gap operator. We give necessary and sufficient conditions on the left, right reflection coefficient such that the difference of the potentials has finite ...
Egorova, Iryna, Teschl, Gerald
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Symmetries and reductions of integrable nonlocal partial differential equations
, 2019 In this paper, symmetry analysis is extended to study nonlocal differential equations, in particular two integrable nonlocal equations, the nonlocal nonlinear Schr\"odinger equation and the nonlocal modified Korteweg--de Vries equation.
Peng, Linyu
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Taking limits in topological recursion
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (straightforward‐to‐use) conditions for checking when the commutation with limits holds, thereby closing a ...
Gaëtan Borot +4 more
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Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract In this work, we present a comprehensive theory of stochastic integration with respect to arbitrary cylindrical Lévy processes in Hilbert spaces. As cylindrical Lévy processes do not enjoy a semimartingale decomposition, our approach relies on an alternative approach to stochastic integration by decoupled tangent sequences.
Gergely Bodó, Markus Riedle
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On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces [PDF]
, 2010 We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schr\"odinger equation, the $k$-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces $H^s(\R^n)\cap L^2 ...
Nahas, Joules, Ponce, Gustavo
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On integrability of one third-order nonlinear evolution equation
, 2003 We study one third-order nonlinear evolution equation, recently introduced by Chou and Qu in a problem of plane curve motions, and find its transformation to the modified Korteweg - de Vries equation, its zero-curvature representation with an essential ...
Chou +8 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12427-12439, August 2025.ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods.
Sol Sáez
wiley +1 more source
Reconfiguration of Independent Transversals
Random Structures &Algorithms, Volume 67, Issue 1, August 2025.ABSTRACT Given integers Δ≥2$$ \Delta \ge 2 $$ and t≥2Δ$$ t\ge 2\Delta $$, consider a graph of maximum degree Δ$$ \Delta $$ and a partition of its vertices into blocks of size at least t$$ t $$. By a seminal result of Haxell, there is an independent set of the graph that is transversal to the blocks, a so‐called independent transversal. We show that, if
Pjotr Buys, Ross J. Kang, Kenta Ozeki
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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.
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