A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
In this paper,the convergence and stability of the ’Leap-frog’ finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the n...In this paper,the convergence and stability of the ’Leap-frog’ finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).展开更多
For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the metho...For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.展开更多
Following & recent paper of the authors in Communications in Partial Differential Equa- tions, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed c...Following & recent paper of the authors in Communications in Partial Differential Equa- tions, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.展开更多
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
文摘In this paper,the convergence and stability of the ’Leap-frog’ finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).
基金Supported by the Natural Science Foundation of Ningbo under Grant No. 2008A610029
文摘For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.
基金The first author is supported by the Chinese Youth Foundation and the innovation Funds of theChinese Academy of Sciences. The
文摘Following & recent paper of the authors in Communications in Partial Differential Equa- tions, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
