Abstract
Abstract The investigations of integrability, exact solutions and dynamics of nonlinear partial differential equations (PDEs) are vital issues in nonlinear mathematical physics. In this paper, we derive and solve a new Lax integrable nonisospectral integral-differential system. To be specific, we first generalize an eigenvalue problem and its adjoint equation by equipping it with a new time-varying spectral parameter. Based on the generalized eigenvalue problem and the adjoint equation, we then derive a new Lax integrable nonisospectral integral-differential system. Furthermore, we obtain exact solutions and their reduced forms of the derived system by extending the famous non-linear Fourier analysis method–inverse scattering transform (IST). Finally, with graphical assistance we simulate a pair of reduced solutions, the dynamical evolutions of which show that the amplitudes of solutions vary with time.
Highlights
Introduction the integrability of partial differential equations (PDEs)Usually, it is necessary to indicate the type of integrability [16]
With graphical assistance we simulate a pair of reduced solutions, the dynamical evolutions of which show that the amplitudes of solutions vary with time
It is necessary to indicate the type of integrability [16]
Summary
To derive system (1), firstly we equip the eigenvalue problem [20]:. (2) and (3), the potential functions q = q(x, t) → 0, r = r(x, t) → 0 as x → ±∞, all the derivatives of q and r have the same asymptotic properties, and A = A(x, t, k, q, r), B = B(x, t, k, q, r) and C = C(x, t, k, q, r) are functions of the indicated variables to be determined later. (13)-(15) into Eq (12) yields system (1). This shows that system (1) is Lax integrable
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