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In this letter we propose an approach to obtain solutions for the nonlocal nonlinear Schrödinger hierarchy from the known ones of the Ablowitz-Kaup-Newell-Segur hierarchy by reduction. These solutions are presented in terms of double Wronskian and some of them are new. The approach is general and can be used for other systems with double Wronskian solutions which admit local and nonlocal reduct...

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation KdV7 . A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation w...

An algebraic definition of Gardner’s deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found. Introduction. We consider the problem of constru...

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are ch...

The first part of the paper is devoted to two descriptions all polynomial tau-functions KP hierarchy: by a generalized Jacobi-Trudy formula, and Giambelli formula. We use latter formula in second obtain CKP hierarchy its n-reductions. In particular, for n=3 we find Kaup-Kupershmidt hierarchy.

PURPOSE Somatic growth is an important indicator of health in children. Adequate organ growth is essential in growth and directly related to body growth. We consider renal length as a surrogate of organ growth in growing children. Measurement of weight, height, and many anthropometric indices, such as body surface area (BSA), body mass index (BMI), and Rohrer and Kaup indices, are used to evalu...

This paper was motivated by the observation that after quickly finding a number of hierarchies (mKdV, Sawada-Kotera, Kaup-Kuperschmidt) soon after finding that KdV was integrable, nothing more was found for polynomial scalar evolution equations linear in the highest order derivative. In this paper we prove that under some mild conditions on the equations one can put a uniform bound on the order...

We derive the soliton matrices corresponding to an arbitrary number of higherorder normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix R...

We consider the periodic standing waves in derivative nonlinear Schrodinger (DNLS) equation arising plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all terms of eight eigenvalues Kaup-Newell spectral problem located at end points bands outside real line. The analytical work is complemented numerical approximation bands, this enables us to fully char...