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Properties of large amplitude waves in a relativistic magnetised plasma are studied using the method of reductive perturbation. The plasma under consideration consists of warm adiabatic ions and isothermal warm electrons, under the influence of a magnetic field. A  onsideration of large amplitude waves demands study of the relativistic situation. In the present case we consider both the electrons and ions to be relativistic. A KdV equation is derived from which a nonlinear Schrodinger equation is deduced by further scaling. Lastly we derive an expression for nonlinear wave number shift, critical angle of propagation and the condition for modulational instability. Our analysis is applicable to both laboratory and space plasmas.

Nonlinear Wave Number Shift and Modulational Instability for Large Amplitude Waves in a Relativistic Magnetised Plasma