Vector shock soliton and the Hirota bilinear method

摘要: Abstract The Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction–diffusion equations for n-component vector order parameter, with reaction part in form third polynomial, determined by three distinct constant vectors. representation derived extracting one roots (unstable general), which allows us reduce cubic nonlinearity a quadratic one. solution, implementing transition between other two roots, as fixed points potential from continuum set values, constructed simple way. In our approach, velocity truncating perturbation expansion and it found terms all roots. Shock solitons extensions model, including second time derivative term nonlinear transport are derived. Numerical solutions illustrating generation solitary wave initial step function, depending polynomial given.