Nonlinear wave interaction problems in the three-dimensional case

被引：13

作者：

Curro, C. ^{[1
]}

Manganaro, N. ^{[1
]}

Pavlov, M. V. ^{[2
,3
,4
]}

机构：

[1] Univ Messina, MIFT, Viale Ferdinando Stagno DAlcontres 31, I-98166 Messina, Italy

[2] Russian Acad Sci, Lebedev Phys Inst, Sect Math Phys, Leninskij Prospekt 53, Moscow 119991, Russia

[3] Natl Res Nucl Univ MEPHI, Dept Appl Math, Kashirskoe Shosse 31, Moscow 115409, Russia

[4] Novosibirsk State Univ, Dept Mech & Math, 2 Pirogova St, Novosibirsk 630090, Russia

来源：

NONLINEARITY | 2017年 / 30卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

nonlinear wave interactions; hydrodynamic integrable systems; generalized hodograph method; QUASILINEAR HYPERBOLIC SYSTEMS; RIEMANN INVARIANTS; EXAMPLES;

D O I：

10.1088/1361-6544/30/1/207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Three-dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three-dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous semi-Hamiltonian hydrodynamic type systems (i. e. possess diagonal form and infinitely many conservation laws). The interaction of N waves was studied. In particular we prove that they behave like simple waves and they distort after the collision region. The amount of the distortion can be analytically computed.

引用

页码：207 / 224

页数：18

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