Coherent structures of the phi(4) equation via invariant Painleve analysis
Abbreviated Journal Title
Indian J. Pure Appl. Math.
coherent structures; Painleve analysis; accessibility from initial; conditions; GINZBURG-LANDAU EQUATION; EVOLUTION-EQUATIONS; MARGINAL STABILITY; PERIODIC SOLUTIONS; FRONT PROPAGATION; UNSTABLE STATES; SELECTION; EXPANSIONS; PATTERNS; PULSES; Mathematics
Exact closed-form coherent structures (pulses/fronts/domain walls) having the form of complicated traveling waves are constructed via invariant Painleve analysis for the Phi(4) equation, which belongs to the family of Klein-Gordon equations. These analytical solutions, which are derived directly from the underlying PDE's, are investigated in the light of restrictions imposed by the ODE that any traveling wave reduction of corresponding PDE must satisfy. In particular, it is shown that the coherent structures a) asymptoticaly satisfy the ODE governing traveling wave reductions, and b) are accessible to the PDE from compact support initial conditions. The solutions are compared with each other, and with previously known solutions of the equation.
Indian Journal of Pure & Applied Mathematics
"Coherent structures of the phi(4) equation via invariant Painleve analysis" (2002). Faculty Bibliography 2000s. 3127.