We study the periodic non-linear Schrodinger equation −iu t +u xx = ±|u| p−1 u for initial data which are assumed to be small in some negative order Sobolev space H s (T) (s < 0), but which may have large L 2 mass. In [6], [7] these equations were shown to be ill-posed in H s (T), in the sense that the solution map was not uniformly continuous from H s (T) to itself even for short times and sma...

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Non-local transformation, which connects the 3-dimensional Burgers-type equation with a linear heat equation, is constructed. Via this transformation, nonlinear superposition formulae for solutions are obtained and the conditional non-local symmetry of this equation is studied. The multidimensional generalization of the Burgers equation L1(u) = u0 − u|∇u| − u = 0, (1) is called further the Burg...

ab initio calculations at hf/6-31g* level of theory for geometry optimization and mp2/6-31g*//hf/6-31g* for a single point total energy calculation are reported for the importantenergy-minimum conformations and transition-state geometries of 1, 3-diazacyclohepta-1, 2-diene (2) and 1, 3-diazacycloocta-1, 2-diene (3). the c2 symmetric twist-chair (2-tc)conformation of 2 is calculated to be 7.4 kj...

In this study we find all solutions of the Diophantine equation $B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}}$ in positive integer variables $(n_{1},n_{2},a_{1},a_{2},a_{3}),$ where $B_{n}$ denotes $n$-th balancing number.