Problem of stability of multidimensional solutions of the BK class equations in space plasma

Abstract

© 2018 COSPAR The problem of stability of the multidimensional solutions of the BK class equations describing the nonlinear waves which are forming on the low-frequency branch of oscillations in plasma for cases when β≡4πnT/B2«1 and β>1 is studied. In first case, for ω<ωB=eB/Mc,kλD«1 the FMS waves are excited, and their dynamics under conditions kx2≫k⊥2, vx«cAnear the cone of θ=arctan(M/m)1/2, is described by the equation of the BK class known as the GKP equation for magnetic field h=B∼/B with due account of the high order dispersive correction defined by values of plasma parameters and angle θ=(B,k). In another case, the dynamics of the finite-amplitude Alfvén waves propagating near-to-parallel to B is described by the equation of the same class known as the 3-DNLS equation for h=(By+iBz)/2B|1-β|. To study the stability of multidimensional solutions in both cases the method of investigation of the Hamiltonian bounding with deformation conserving momentum by solving the variation problem is used. As a result, we have obtained the conditions of existence of the 2D and 3D soliton solutions in the BK system for cases of the GKP and 3-DNLS equation (i.e. for the FMS and Alfvén waves, respectively) in dependence on the equations’ coefficients, i.e. on the parameters of both plasma and wave.