New spiky solitary waves, explosive modes and periodic progressive waves in a magnetised plasma

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Abstract
A new class of nonlinear evolution equations presented here A(d phi /d eta )2=c1 phi 2+(4/5)c2 phi 52/+(2/3)c3 phi 3+(4/7) c4 phi 7/2 describes the one-dimensional wave propagation of ion acoustic waves in a magnetised plasma with trapped electrons. A, c1, c2, c3, c4 are arbitrary constants. The remarkable feature of this equation is that a higher-order nonlinear term of phi 7/2 appears in this equation. It is found that this equation has a new type of spiky solitary-wave solution, an explosive (bursting) solution and periodic progressive-wave solutions. The explosive solution is associated with the wave with the negative potential. Periodic progressive-wave solutions are reduced to the spiky solitary wave and the explosive solution under a certain condition. This theory may be applicable to explaining the behaviour of higher-order nonlinear waves in physical systems.