A Lagrangian for strongly nonlinear unsteady water waves ~including overturning waves! is obtained. It is shown that the system of quadratic equations for the Stokes coefficients, which determine the shape of a steady wave ~discovered by Longuet-Higgins 100 years after Stokes derived his system of cubic equations! directly follows from the canonical system of Lagrange equations. Applications to...

We study the instability of algebraic solitons for integrable nonlinear equations in one spatial dimension that include modified KdV, focusing NLS, derivative NLS, and massive Thirring equations. We develop the analysis of the Evans function that defines eigenvalues in the corresponding Lax operators with algebraically decaying potentials. The standard Evans function generically has singulariti...

The quadratic matrix equation AX2 + B X +C = 0 in n ×n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration m...

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

We study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The quadratic and reducible cubic polynomials are completely understood, while in the irreducible cubic case, we give a family of polynomials with the bound which is the best currently known.

The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type f(x + y) + f(x − y) = 2g(x) + 2h(y), x ⊥ y is established where ⊥ is a symmetric orthogonality in the sense of Rätz and f is odd. ∗2000 Mathematics Subject Classification. Primary 39B52, secondary 39B82.

Topology preservation and detection is a well known concept in the processing of 2and 3-dimensional binary images. These images can be considered as sets that are mapped on square tessellated (hyper cubic) grids. This paper describes how the formalisms derived for 2D and 3D images can be expanded to N-dimensional images, i.e. binary point sets that are aligned on an N-dimensional square tessell...

We study the Isomorphism of Polynomial (IP2S) problem with m = 2 homogeneous quadratic polynomials of n variables over a finite field of odd characteristic: given two quadratic polynomials (a,b) on n variables, we find two bijective linear maps (s, t) such that b = t◦a◦s. We give an algorithm computing s and t in time complexity Õ(n) for all instances. The IP2S problem was introduced in cryptog...