By the recursion operator of the Kaup–Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit c→∞ it reduces to DNLS equation and preserves integrability at any order of relativistic corrections. The compact explicit representation of the linear problem for this equation becomes possible due to notions of the q-...

In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . . . , am, b1, . . . , bm) = (a1, . . . ,...

We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is...

We construct a new series of multicomponent integrable PDE systems that contain as particular example (with appropriately chosen parameters) many famous including KdV, coupled Harry Dym, Camassa-Holm, Kaup-Boussinesq systems. The contains also with no low-component analogues.

The larvae of Didimus africanus (Percheron), D. haroldi Kuwert, D. alvarodoi (?) Corella, D. parastictus (Imhoff), D. nachtigali Kuwert, Erionomus planiceps (Esch.), E. pilosus Arrow, Taeniocerus pygmaeus (Kaup) and Comacupes basalis (Smith) are described for the first time. Larvae of Leptaulax bicolor (F.), L. dentatus (F.) and Aceraius grandis (Burm.) are redescribed and compared with previou...

Two integrable counterparts of the D-Kaup–Newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal Lie algebra soð3;RÞ. An application of the trace identity presents Hamiltonian or quasiHamiltonian structures of the resulting counterpart soliton hierarchies, thereby showing their Liouville integrability, i.e., the existence...