A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the s...

We discuss Hamiltonian formulations for integrable couplings, particularly biand tri-integrable couplings, based on zero curvature equations. The basic tools are the variational identities over non-semisimple Lie algebras consisting of block matrices. Illustrative examples include dark equations and biand tri-integrable couplings of the KdV equation and the AKNS equations, generated from the en...

The algebraic structures of zero curvature representations are furnished for multilayer integrable couplings associated with matrix spectral problems, both discrete and continuous. key elements a class loop algebras consisting block matrices blocks the same size. As illustrative examples, isospectral non-isospectral corresponding commutator relations their Lax operators computed explicitly in c...

Modifications of the non-linear Schr\"odinger model (MNLS) $ i \partial_{t} \psi(x,t) + \partial^2_{x} - [\frac{\delta V}{\delta |\psi|^2} ] = 0,$ where $\psi \in C$ and $V: R_{+} \rightarrow R$, are considered. We show that MNLS models possess infinite towers quasi-conservation laws for soliton-type configurations with a special complex conjugation, shifted parity delayed time reversion (${\ca...

سابقه و هدف: آب هوای یک منطقه در دوره بلندمدت را اقلیم گویند. شناسایی طبقه‌بندی اقلیمی از دیرباز مورد توجه متخصصان هواشناسی بوده است. محققان با به کارگیری روش ­های مختلف استفاده متغیرهای همچون بارش دما، زمین مناطق همگن طبقه ­بندی کرده‌اند نتایج پهنه‌بندی ارزیابی کمبود منابع مقیاس­ های کوچک بزرگ منظور پیش‌بینی اقدامات عملی برای کنترل خشکی آسیب‌پذیر به‌کار برده‌اند. هدف این تحقیق به‌‌روزرسانی تحل...

A discrete analog of a skew selfadjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenbe...

Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces parameter ? with its complex conjugate ??, and other one nonlocal, negative ???. Riemann–Hilbert problems thus inverse scattering transforms formulated from...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...