We consider scalar (1 + 1)-dimensional evolution equation of order n ≥ 2, which possesses time-independent formal symmetry (i.e. it is integrable in the sense of symmetry approach), shared by all local generalized time-independent symmetries of this equation. We show that if such equation possesses the nontrivial canonical conserved density ρm, m ∈ {−1, 1, 2, . . .}, then it has no polynomial i...

In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem is transformed into corresponding Riemann-Hilbert on basis Lax pair and scattering matrix. After that problems are converted through a decomposition matrix-valued spectral function factorizations jump matrix for problem. Finally, by solving l...

We show that the supersymmetric nonlinear Schrödinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they con...