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We consider a modification of the K(2,2) equation ut=2uuxxx+2kuxuxx+2uux using the bifurcation method of dynamical systems and the method of phase portraits analysis. From dynamic point of view, some peakons, solitary,and smooth periodic waves are found and their exact parametric representations are presented. Also, the coexistence of peakon and solitary wave solutions is investigated

journal of applied mathematics

Peakon, Solitary and Smooth Periodic Wave Solutions for a Modification of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2,2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Equation

Peakon, Solitary and Smooth Periodic Wave Solutions for a Modification of theK(2,2)Equation