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A nonlinear PDE combining with a new fourth-order term    D    x    2D    t    2    is studied. Adding three new fourth-order derivative terms and some second-order derivative terms, we formulate a combined fourth-order nonlinear partial differential equation, which possesses a Hirota’s bilinear form. The class of lump solutions is constructed explicitly through Hirota’s bilinear method. Their dynamical behaviors are analyzed through plots.

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Lump Solutions of a Nonlinear PDE Combining with a New Fourth-Order Term<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>∗</mml:mo></mml:math>

Lump Solutions of a Nonlinear PDE Combining with a New Fourth-Order TermDx2Dt2∗