Solutions of the Hamilton--Jacobi equation for one component two\n dimensional Field Theories

1995/01/25 by Wulf Boettger, Boettger, Wulf, Henning Wissowski +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.hep-th/9501115

Abstract

The Hamilton--Jacobi formalism generalized to 2--dimensional field theories\naccording to Lepage's canonical framework is applied to several covariant real\nscalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville\nand \φ⁴ theories. For simplicity we use the Hamilton--Jacobi equation of\nDeDonder and Weyl. Unlike mechanics we have to impose certain integrability\nconditions on the velocity fields to guarantee the transversality relations\nbetween Hamilton--Jacobi wave fronts and the corresponding families of\nextremals embedded therein. B "acklund Transformations play a crucial role in\nsolving the resulting system of coupled nonlinear PDEs.\n

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