Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation. Using zero-seed solutions, 1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation, along with the expression for N-soliton solutions. Influence of coefficients that are taken as a function of time instead of a constant, i.e., coefficient function δ(t), on the solutions is investigated by choosing the coefficient function δ(t), and the dynamics of the solutions are analyzed. This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations. The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.