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MP: Theoretische und Mathematische Grundlagen der Physik

MP 10: Poster

MP 10.3: Poster

Dienstag, 8. März 2005, 13:00–16:00, Poster TU B

Elliptic solutions of some nonlinear wave and evolution equations and their linear superposition — •Julia Nickel and Hans Werner Schürmann — FB Physik, Universität Osnabrück

A method is presented for finding a subset of the exact (traveling-wave) solutions of various nonlinear wave and evolution equations (NLWEE).

By using an appropriate transformation ψ→ f the NLWEE is transformed into an ordinary differential equation (f_x)²=R, where R is a fourth degree polynomial in f. The solutions of this differential equation are expressed in terms of Weierstrass’s elliptic function ℘ and include periodic and solitary-wave-like solutions (No-dqelliptic solution No-dq) [1]. By suitable linear superposition of particular periodic elliptic solutions additional solutions of the NLWEE can be generated [2].

The aim of the project is to investigate various nonlinear wave and evolution equations with respect to the existence of elliptic solutions and the possibility to enlarge the solution set by superposition.

[1] K. Weierstrass, Mathematische Werke V, (Johnson, New York, 1915), pp. 4-16.

[2] A. Khare and U. Sukhatme, J. Math. Phys., 43 (2002).