Titlebook: Introduction to Multidimensional Integrable Equations; The Inverse Spectral B. G. Konopelchenko,C. Rogers Book 1992 Springer Science+Busine

CANDY

持久

engagement

,General Methods for the Construction of (2+1)-Dimensional Integrable Equations. τ-Function and ∂̄-Drelies on the existence of an appropriate linear system whose compatibility condition is equivalent to the nonlinear system under consideration. No general criteria for the applicability of the IST method to a nonlinear system are presently available. Accordingly, each specific case requires a separate investigation.

树木心

Multidimensional Integrable Systems,t multidimensional nonlinear equation integrable by the IST method is the self-dual (or anti-self dual) equation of Yang-Mills theory, namely, .where .. is the stress-tensor of the Yang-Mills field and .is the tensor dual to ... Here, ... is the usual antisymmetric constant tensor.

净礼

乐章

Other Integrable Equations and Methods of Solution in 2+1 Dimensions,Models which describe the resonant interaction of wave packets are of great interest in physics. Such resonant interaction arises, for instance, in the case of three waves if the conditions .where . are the wave vectors and .. are the frequencies of the waves, are simultaneously satisfied.

Asperity

Plenum Monographs in Nonlinear Physicshttp://image.papertrans.cn/i/image/473942.jpg

profligate

a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which common

流浪

Introduction,ollowing interaction without change of shape. Indeed their speed is likewise unaltered [3]. An attempt to understand these unexpected and astonishing experimental facts led, two years later, to the discovery of the inverse scattering transform method for the analysis of nonlinear equations such as the KdV equation which possess solitonic behavior.

分解

Conclusion,(1 + l)-dimensional case, and there remains much to be understood. Nevertheless, to conclude, we indicate certain important papers in these areas so that the interested reader may consult them directly.