On Painlevé Analysis, Symmetry Group and Conservation Laws of Date–Jimbo–Kashiwara–Miwa Equation

In this study, the Painlevé property of Date–Jimbo–Kashiwara–Miwa equation is verified with WTC approach and the exact soliton solution is obtained using Pickering’s algorithm. We find the Lie point symmetries and three independent similarity reductions. Further, two different techniques are employed independently to construct conservation laws. Multipliers in the direct method have given the infinite number of non-trivial local conservation laws and self-adjointness of equation helped us to construct infinite local conservation laws associated with Lie symmetries. The existence of the infinite number of local conservation laws strongly justifies the complete integrability of equation. © 2018, Springer (India) Private Ltd., part of Springer Nature.