The Cauchy problem for the Pavlov equation with large data

被引：2

作者：

Wu, Derchyi ^{[1
]}

机构：

[1] Acad Sinica, Inst Math, Taipei, Taiwan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 03期

关键词：

KADOMTSEV-PETVIASHVILI EQUATION; DISPERSIONLESS KP HIERARCHY; EINSTEIN-WEYL SPACES; HEAVENLY EQUATION; INTEGRABLE SYSTEM; WAVE-EQUATIONS; TWISTOR-THEORY; VECTOR-FIELDS; DKP EQUATION;

D O I：

10.1016/j.jde.2017.03.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a local solvability of the Cauchy problem for the Pavlov equation with large initial data by the inverse scattering method. The Pavlov equation arises in studies Einstein-Weyl geometries and dispersion less integrable models. Our theory yields a local solvability of Cauchy problems for a quasi-linear wave equation with a characteristic initial hypersurface. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1874 / 1906

页数：33

共 50 条

[21] A Cauchy problem for an ultrahyperbolic equation
Kostomarov, DP
DIFFERENTIAL EQUATIONS, 2002, 38 (08) : 1155 - 1161
[22] Cauchy problem for the Ostrovsky equation
Varlamov, V
Liu, Y
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2004, 10 (03) : 731 - 753
[23] On the cauchy problem for the einstein equation
Lychagin, V. V.
Yumaguzhin, V. A.
DOKLADY MATHEMATICS, 2012, 86 (03) : 781 - 783
[24] A Cauchy problem for the Tartar equation
Sazhenkov, S
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2002, 132 : 395 - 418
[25] The Cauchy problem for the Novikov equation
Wei Yan
Yongsheng Li
Yimin Zhang
Nonlinear Differential Equations and Applications NoDEA, 2013, 20 : 1157 - 1169
[26] Cauchy problem for ultrahyperbolic equation
Doklady Akademii Nauk, 2002, 382 (05) : 598 - 602
[27] The Cauchy problem for the Ishimori equation
Sung, LY
JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 139 (01) : 29 - 67
[28] On the cauchy problem for the einstein equation
V. V. Lychagin
V. A. Yumaguzhin
Doklady Mathematics, 2012, 86 : 781 - 783
[29] ON CAUCHY PROBLEM FOR LAPLACE EQUATION
Khasanov, A. B.
Tursunov, F. R.
UFA MATHEMATICAL JOURNAL, 2019, 11 (04): : 91 - 107
[30] The Cauchy problem for the Rosenau equation
Wang, Shubin
Xu, Guixiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (1-2) : 456 - 466

← 1 2 3 4 5 →