A Class Of Quasilinear Equation Triangular Form Unchanged Since Space Research

To study trigonometric invariant subspaces which allowed by the kind of quasilinear equations with the form of We take the sine and cosine invariant subspaces into these evolution equations and analysis the different coefficient conditions on k with different values. When k is even, the equations allow the sine invariant subspace and cos/sin-invariant subspace if these equations allow cosine invariant subspace.In the first chapter, the background of this paper is introduced as well as some important results obtained by the previous studies.In chapter two, we study three common invariant subspaces:polynomial, trigonometric, exponential which satisfied by the kind of quasilinear equations with the form of and illustrate the application method of invariant subspace to get the exact solutions of some equations.In chapter three and four, we discuss this class of evolution equations in odd-order and even-order, verify the cosine invariant subspace which allowed by the evolution equations, then analogue sine/cosine form of invariant subspaces, draw some useful conclusions.At last, we conclude the paper and explore some open problems about the kind of quasilinear equations.