Comments on the perturbed sine–Gordon equation

Comments on the Equation ±ra

in nonnegative integers x, y and integers u, v ∈ {0, 1}. Note that the choice of x and y uniquely determines the choice of u and v, so we will usually refer to a solution (x, y). The Case (ra, sb) = 1 There are only a finite number of cases with N > 3 solutions to Equation (P) [23]. There are at least five infinite families of cases with N = 3 solutions to (P), as well as a number of anomalous ...

Comments on the equation ± ra x ±

in nonnegative integers x, y and integers u, v ∈ {0, 1}. Note that the choice of x and y uniquely determines the choice of u and v, so we will usually refer to a solution (x, y). The Case (ra, sb) = 1 There are only a finite number of cases with N > 3 solutions to Equation (P) [14]. There are at least five infinite families of cases with N = 3 solutions to (P), as well as a number of anomalous ...

99 Comments on Lagrange Partial Differential Equation

The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products consisting of a scalar function, a homogeneous first order differential operator and the reciprocal of the scalar function. The factorization procedure is utiliz...

Linearizability of the Perturbed Burgers Equation

We show in this letter that the perturbed Burgers equation ut = 2uux + uxx + ǫ ( 3α1u 2 ux + 3α2uuxx + 3α3u 2 x + α4uxxx ) is equivalent, through a near-identity transformation and up to O(ǫ), to a linearizable equation if the condition 3α1 − 3α3 − 3 2 α2 + 3 2 α4 = 0 is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to...

Perturbed bifurcations in the BCS gap equation.