Qualitative properties of solutions for linear and nonlinear hyperbolic PDE's

Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanhand sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi’s elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential eq...

Symbolic Computation and the Extended Hyperbolic Function Method for Constructing Exact Traveling Solutions of Nonlinear PDEs

On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, th...

Linear and Nonlinear Eigenproblems for PDEs

The workshop discussed the numerical solution of linear and nonlinear eigenvalue problems for partial differential equations. It included the theoretical analysis the development of new (adaptive) methods, the iterative solution of the algebraic problems as well as the application in many areas of science and engineering. Mathematics Subject Classification (2000): 65N25, 65F15, 15A18. Introduct...

Solutions to Problems for Quasi-Linear PDEs

(a) At what time ts and position xs does a shock first form? (b) Identify the important values of s and find the corresponding characteristics. Sketch the characteristics and indicate the region in the xt-plane in which the solution is well-defined (i.e. does not break down). (c) Construct tables as in class for the x and u values at the important values of s for times t = 0, 2/3, 4/3. Use thes...

Construction and Qualitative Behavior of Solutions for a System of Nonlinear Hyperbolic Conservation Laws with Damping