1998/05/19 by E. P. Raposo, Ernesto P. Raposo, D. Bazeia
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Burgers' equation #Dispersion (optics) #Dispersionless equation #Geometry #Kadomtsev–Petviashvili equation #Korteweg–de Vries equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Physics #Polynomial #Quantum mechanics #Scalar (mathematics) #Scalar field #Soliton #cond-mat #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1016/s0375-9601(99)00067-5
11 pages, Latex
arxiv created 1998/05/19 · openalex publication_date 1999/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe exact kink soliton solutions to nonlinear partial differential equations in the generic form ut + P(u) ux + νuxx + δuxxx = A(u), with polynomial functions P(u) and A(u) of u=u(x,t), whose generality allows the identification with a number of relevant equations in physics. We emphasize the study of chirality of the solutions, and its relation with diffusion, dispersion, and nonlinear effects, as well as its dependence on the parity of the polynomials P(u) and A(u) with respect to the discrete symmetry u→-u. We analyze two types of kink soliton solutions, which are also solutions to 1+1 dimensional phi4 and phi6 field theories.