[en] We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an abstract setting, where the operators in an evolution equation represent the unknowns. We also prove Fréchet-differentiability and local ill-posedness for this problem. We then demonstrate how to apply this theory to actual problems by two example equations motivated by linear elasticity and electrodynamics. For these problems it is even possible to obtain a simple characterization of the adjoint of the Fréchet-derivative of the forward operator, which is of particular interest for the application of regularization schemes. (paper)

[en] It is shown that, in four dimensions, it is possible to introduce coordinates so that an analytic metric locally takes block diagonal form, i.e. one can find coordinates such that g_αβ = 0 for (α, β) in S where S = {(1, 3), (1, 4), (2, 3), (2, 4)}. We call a coordinate system in which the metric takes this form a 'doubly biorthogonal coordinate system'. We show that all such coordinate systems are determined by a pair of coupled second-order partial differential equations.

[en] In this paper we extend some properties of analytic functions on several complex variables to solutions of overdetermined systems of complex partial differential equations. It is proved that many global properties of analytic functions are true for solutions of the Vekua system in special cases. The relation between analytic functions and solutions of quasi-linear systems is discussed in the paper. (author). 8 refs

[en] A simple proof of Magnus' Freiheitsatz for one-relator groups is given which can be easily applied with slight modifications to prove a generalization of the theorem to any number of relators. (author). 10 refs

[en] We show that the the integrable subclasses of the equations q_t = f(x, t)q₃ + H(x, t, q, q₁) are the same as the integrable subclasses of the equations q_t = q₃ + F(q, q₁). (orig.)

[en] We show that one can devise through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole–Hopf transformation. If the equation is linearizable, then the symmetry provides the linearizing transformation. At the end, we present a few examples of applications for equations defined on four lattice points. (paper)

[en] We introduce a bracket on 1-forms defined on J^∞(S¹,Rⁿ), i.e. the infinite jet extension of the space of loops, and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that certain hierarchies appearing in the framework of F-manifolds with a compatible flat connection (M, ∇, ○) are Hamiltonian in a generalized sense. Moreover, we show that if a metric g compatible with ∇ is also invariant with respect to ○, then this generalized Hamiltonian setup reduces to the standard one. (paper)

[en] Geometric prolongation structures for the Kp equations in (2 + 1) dimensions is studied. The Author make use of its reductions to (1 + 1)-dimensional integrable systems given by Cheng, to obtain these structures using Morris method for geometric prolongations in higher dimensions. New unified prolongation structures for the Kp equations are obtained via this study

[en] The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

[en] The authors present a method to solve a large class of second order systems of partial differential equations on a vector superspace. Some examples are presented and discussed