Results 21 to 30 of about 2,221 (63)

Wave Solutions

, 2012
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be understood as a ...
Christov, Ivan C.
core   +1 more source

Nonlinear PDEs for gap probabilities in random matrices and KP theory [PDF]

, 2012
Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related
Adler, Adler, Adler, Adler, Adler, Adler, Adler, Adler, Bergère, Bertola, Bertola, Bleher, Borodin, Brézin, Brézin, Brézin, Brézin, Claeys, Date, Date, Harnad, Helminck, Johansson, Johansson, Kac, Krichever, M. Adler, M. Cafasso, Miwa, Okounkov, P. van Moerbeke, Prähofer, Rumanov, Rumanov, Segal, Tracy, Tracy, Tracy, van de Leur, Wasow, Widom   +40 more
core   +3 more sources

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, EarlyView.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools

, 2014
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media.
Kschischang, Frank R., Yousefi, Mansoor I.   +1 more
core   +1 more source

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

Tau functions as Widom constants

, 2017
We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood.
Chang-Duk Jun, Nam Hoon Cho, Sang A Park, Sang-Uk Seo, Sung Hwan Lee, Woo Jung Lee, Young-Min Hyun, Yunyun Zou   +7 more
core   +2 more sources

Heisenberg‐smooth operators from the phase‐space perspective

Mathematische Nachrichten, Volume 298, Issue 8, Page 2845-2866, August 2025.
Abstract Cordes' characterization of Heisenberg‐smooth operators bridges a gap between the theory of pseudo‐differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase‐space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general ...
Robert Fulsche, Lauritz van Luijk
wiley   +1 more source

On the Inverse Scattering Method for Integrable PDEs on a Star Graph [PDF]

, 2015
© 2015, Springer-Verlag Berlin Heidelberg. We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary
A. Boutet De Monvel, A. Doikou, A.R. Aguirre, A.S. Fokas, A.S. Fokas, A.S. Fokas, C.S. Gardner, D. Faddeev Ludwig, D. Noja, E. Corrigan, E.K. Sklyanin, F. Demontis, I. Habibullin, I.T. Habibullin, J. Avan, J. Avan, J. Holmer, J.F. Gomes, M. Mintchev, M.J. Ablowitz, M.J. Ablowitz, P. Bowcock, P. Deift, P. Deift, P.D. Lax, R. Adami, R.F. Bibkaev, R.R. Rosales, S. Albeverio, S. Manakov, V. Caudrelier, V. Caudrelier, V. Caudrelier, V. Kostrykin, V.E. Zakharov, V.O. Tarasov, Vincent Caudrelier   +36 more
core   +2 more sources

On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates

Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.
Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri   +2 more
wiley   +1 more source

On the dispersionless Kadomtsev-Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking

, 2011
We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional waves in n+1 dimensions, and arising in several physical
Abramowitz, Dodd R K, Kadomtsev B B, Kamensky V G, Kodama Y, Manakov S V, Manakov S V, Manakov S V, P M Santini, S V Manakov, Timman R, Witham J B, Zakharov V E, Zobolotskaya E A   +13 more
core   +1 more source