In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solit...In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solitary wave solutions are obtained. Then it is substituted into the (2 + 1)-dimensional BLMP equation and (2 + 1)-dimensional KDV equation as an auxiliary equation. Many types of solitary wave solutions are obtained by choosing different coefficient p<sub>1</sub> and q<sub>1</sub> in the Riccati equation, and some of them have not been found in other documents. These solutions that we obtained in this paper will be helpful to understand the physics of the NLEEs.展开更多
The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms...The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.展开更多
文摘In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solitary wave solutions are obtained. Then it is substituted into the (2 + 1)-dimensional BLMP equation and (2 + 1)-dimensional KDV equation as an auxiliary equation. Many types of solitary wave solutions are obtained by choosing different coefficient p<sub>1</sub> and q<sub>1</sub> in the Riccati equation, and some of them have not been found in other documents. These solutions that we obtained in this paper will be helpful to understand the physics of the NLEEs.
文摘The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.
