A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy. Consider the Dirac equation of an electron

We investigate the long-time asymptotics for solutions to Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The present paper is subsequent work our previous [arXiv:2108.03650], which gives soliton resolution mKdV in central asymptotic sector $\{(x,t): \vert \xi \vert<6\}$ $\xi:=x/t$. In paper, via Riemann-Hilbert (RH) associated problem, s...

For a particular class of integral operators K we show that the quantity φ := log det (I +K)− log det (I −K) satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

Abstract We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular motion of planar curves.

Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in context a new variational problem with two constraints. The advantage this is that its nondegenerate local minimizers stable time evolution mKdV equation, whereas saddle points unstable. We explore analytical representation periodic given by Jacobi elliptic functions and compute numerically critical constrained p...

We find one- and two-soliton solutions of shifted nonlocal NLS MKdV equations. discuss the singular structures these soliton present some graphs them.