一类非线性耗散方程组的不变子空间及其精确解

Invariant Subspaces and Exact Solutions to Systems of Nonlinear Dissipative Equations

利用不变子空间方法研究一类在孤立子理论中具有广泛应用的非线性耗散方程组,确定出非线性耗散方程组在它所容许的不变子空间W3^1×W2^2中的完全分类,构造了方程组的精确解或者将方程组约化为有限维动力系统.文中的结果进一步推广了不变子空间理论在非线性偏微分方程中的应用.

In this paper,we apply the invariant subspace method to discuss a class of system to nonlinear dissipative equations arising from soliton theory.We derive a full classifications of invariant subspace W3^1 × W2^2 admitted by nonlinear dissipative systems and construct the exact solutions of these systems or reduce them to finite-dimensional dynamical system.The obtained results further extend the applications of invariant subspace theory in the PDEs.