In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem...In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem.展开更多
A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely...A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.展开更多
The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra ...The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.展开更多
基金supported by the National Natural Science Foundation of China(No.11271079)
文摘In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem.
基金Supported by National Natural Science Foundation of China under Grant Nos.11171312 and 11126308Science and Technology Research Key Projects of the Education Department of Henan Province under Grant No.12A110023
文摘A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.
基金Supported by the National Natural Science Foundation of China under Grant No.11001250
文摘The Hirota-Satsuma coupled KdV equations associated 2 x 2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.
