Reflection of nonlinear solitary waves (mKdV solitons) at critical density of negative ions in a magnetized cold plasma

The reflection of ion acoustic solitons in a magnetized inhomogeneous plasma having positive ions, negative ions and electrons is studied theoretically at the critical density of negative ions, where both compressive and rarefactive solitons are found to exist. Relevant modified Korteweg–deVries (mKdV) equations corresponding to two oppositely moving solitons are coupled to obtain a variable coefficient coupled mKdV equation, which is further solved to obtain the expression of amplitude and width of the reflected solitons. The effect of magnetic field B0, its obliqueness θ (angle between the directions of magnetic field and wave propagation) and negative to positive ion density ratio d0 on the amplitude and width of the reflected solitons together with the reflection coefficient are investigated. A comparison is made between the incident and reflected solitons and it is found that the compressive (rarefactive) solitons are downshifted (upshifted) after the reflection.