The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV hierarchy both positive and negative is generated by the kernel elements of Lenard’s operators pair and recursion operator. Through solving a key operator equation, ...

In this paper, negatons, positons and complexiton solutions of higher order for a non-isospectral MKdV equation, the MKdV equation with loss and nonuniformity terms are obtained through the bilinear Bäcklund transformation. AMS Subject Classification: 35Q53

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

هدیکچ هقباس و فده : ناطرس زا بسانم تاعلاطا اب یم صاخ یئایفارغج هیحان رد فلتخم یاه همانرب ناوت ار یبط یاه یارب لابرغ و نامرد یرگ ) Screening ( هورگ دومن صخشم رطخرپ یاه . نآ زا هک اج گرم نازیم نانمس ناتسا تشادهب زکرم لااب ریم و ی زکرم رد یناقوف شراوگ هاگتسد ناطرس رثا رب ار ی ا هدرک شرازگ ناریا تس . یماـمت تـبث و یـسررب یارـب تفریذپ ماجنا یعماج قیقحت نانمس ناتسا یموب تیعمج نیب رد ناطرس دراوم ...

The spectral transformation technique for symmetric RII polynomials is developed. Use of this technique reveals that the nonautonomous discrete modified KdV (nd-mKdV) lattice is directly connected with the RII chain. Hankel determinant solutions to the semi-infinite nd-mKdV lattice are also presented.

In this paper, we study the time variable coefficient modified Korteweg-de Vries (mKdV) equation from group-theoretic point of view. We obtain Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary variable coefficients. Finally, the solitary ...

We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the solution of the mKdV equation when the dispersive parameter is small. The oscillations are referred to as dispersive shocks. The Whitham equations for the mKdV eq...

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from groupinvariant flows of non-stretching curves in constant curvature manifolds and Lie group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming ...

This work concerns itself on two new coupled mKdV systems, the first with time-dependent coefficients, and the second with constant coefficients. The soliton ansatz will be used for the first system to obtain 1-bright soliton solution. The simplified form of the bilinear method will be used to derive multiple-soliton solutions and multiple singular soliton solutions for the second coupled mKdV ...