We study the long time asymptotic behavior for the Cauchy problem of the modified
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …

Long-time Asymptotics for the Camassa–Holm Equation Page 1 Copyright © by SIAM.
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In this paper, we address the Painlevé asymptotics of the solution in two transition regions
for the defocusing nonlinear Schrödinger (NLS) equation with finite density initial data iqt+ q …

We study the long-time asymptotic behavior of the focusing Fokas-Lenells (FL) equation ux
t+ α β 2 u− 2 i α β ux− α uxx− i α β 2| u| 2 ux= 0 with generic initial data in a Sobolev space …

We present an inverse scattering transform approach to the Cauchy problem on the line for
the Degasperis--Procesi equation $ u_t-u_ {txx}+ 3\omega u_x+ 4uu_x= 3u_xu_ {xx}+ uu …

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of
an extended modified KdV equation with decaying initial data in two transition regions …

We present an inverse scattering transform approach for the equation $ u_ {txx}-3u_x+
3u_xu_ {xx}+ uu_ {xxx}= 0$. This equation can be viewed as the short wave model for the …

The long-time asymptotics of solution to the integrable matrix modified Korteweg–de Vries
equation with a 4× 4 Lax pair on the line in the case of decaying initial data is established …

We develop the inverse scattering transform method for the Novikov equation $ u_t-u_ {txx}+
4u^ 2u_x= 3u u_xu_ {xx}+ u^ 2u_ {xxx} $ considered on the line $ x\in (-\infty,\infty) $ in the …

We discuss direct and inverse spectral theory for the isospectral problem of the
dispersionless Camassa–Holm equation, where the weight is allowed to be a finite signed …