Abstract
In this paper, an integrable KP equation is studied using symmetry and conservation laws. First, on the basis of various cases of coefficients, we construct the infinitesimal generators. For the special case, we get the corresponding geometry vector fields, and then from known soliton solutions we derive new soliton solutions. In addition, the explicit power series solutions are derived. Lastly, nonlinear self-adjointness and conservation laws are constructed with symmetries.
Highlights
It is well known that Kadomtsev–Petviashvili (KP) equation is mainly used to describe the nonlinear wave phenomenon
Symmetry [1,2,3, 13,14,15,16,17,18,19] and conservation laws play a key roles in the fields of applied mathematics and physics
3.1 Symmetry reduction Here, we just consider the following case, as other cases can derived in a similar way
Summary
It is well known that Kadomtsev–Petviashvili (KP) equation is mainly used to describe the nonlinear wave phenomenon. Petviashvili in 1970 [5] This equation play a very key role in the field of mathematical physics. In [12], the authors studied (3 + 1)-dimensional generalized KP and BKP (Bogoyavlenskii–Kadomtsev–Petviashvili) equations using the multiple expfunction algorithm. We try to use the symmetry and conservation laws to study this equation. Symmetry [1,2,3, 13,14,15,16,17,18,19] and conservation laws play a key roles in the fields of applied mathematics and physics.
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