Department Of Mathematics And Statistics
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Item Doubly periodic wave structure of the modified Schr�dinger equation with fractional temporal evolution(Elsevier B.V., 2022-01-01T00:00:00) Kumari, Pinki; Gupta, R.K.; Kumar, Sachin; Nisar, K.S.Abundant Jacobi elliptic type solutions with distinct physical structures of complex nonlinear conformable time-fractional modified Schr�dinger equation are obtained by using the generalized Jacobi elliptic function (GJEF) method. The Jacobi function expansions may lead to new doubly periodic wave solutions, soliton solutions, and triangular periodic solutions. Nowadays the conformable operator is being used for a better description of the dynamical systems. Motivated by the potential applications of the governed equation in nonlinear optics, biological sciences, and fluid dynamics, these solutions may be significant in the study of wave propagation in the desired field. Symbolic computations are made with the aid of Maple. � 2022 The AuthorsItem A new Painlev� integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws(Emerald Publishing, 2021-05-05T00:00:00) Kumar, Sachin; Gupta, Rajesh Kumar; Kumari, PinkiPurpose: This study aims to find the symmetries and conservation laws of a new Painlev� integrable Broer-Kaup (BK) system with variable coefficients. This system is an extension of dispersive long wave equations. As the system is generalized and new, it is essential to explore some of its possible aspects such as conservation laws, symmetries, Painleve integrability, etc. Design/methodology/approach: This paper opted for an exploratory study of a new Painleve integrable BK system with variable coefficients. Some analytic solutions are obtained by Lie classical method. Then the conservation laws are derived by multiplier method. Findings: This paper presents a complete set of point symmetries without any restrictions on choices of coefficients, which subsequently yield analytic solutions of the series and solitary waves. Next, the authors derive every admitted non-trivial conservation law that emerges from multipliers. Research limitations/implications: The authors have found that the considered system is likely to be integrable. So some other aspects such as Lax pair integrability, solitonic behavior and Backlund transformation can be analyzed to check the complete integrability further. Practical implications: The authors develop a time-dependent Painleve integrable long water wave system. The model represents more specific data than the constant system. The authors presented analytic solutions and conservation laws. Originality/value: The new time-dependent Painleve integrable long water wave system features some interesting results on symmetries and conservation laws. � 2021, Emerald Publishing Limited.