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This paper is contributed to explore all possible single peak solutions for the K*(4,1) equation ut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that the K*(4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1) equation

journal of applied mathematics

Peaked and Smooth Solitons for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>4,1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Equation

Peaked and Smooth Solitons forK*(4,1)Equation