We present a new representation of solutions of focusing nonlinear Schrodinger EQUATION (NLS) EQUATION as a quotient of two determinants. We construct families of quasi-rational solutions of the NLS EQUATION depending on two parameters, a and b. We construct, for the first time, analytical expressions of Peregrine breather of order 7 and multi-rogue waves by deformation of parameters. These expressions make possible to understand the behavior of the solutions. In the case of the Peregrine breather of order 7, it is shown for great values of parameters a or b the appearance of the Peregrine breather of order 5.

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrodinger EQUATION (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS EQUATION as a quotient of two determinants by an exponential depending ont. This formulation gives in the case of the order 3 and 4, solutions with, respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.

In this paper, the fuzzy MATRIX EQUATION AeX B = e C in which A; B are n × n crisp matrices respectively and e C is an n×n arbitrary LR fuzzy numbers MATRIX, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a suffcient condition for the existence of strong fuzzy solution is derived. Some examples are given to illustrate the proposed method.

The main aim of this paper intends to discuss the solution of fuzzy Sylvester MATRIX EQUATION AX+XB=C where A= (aij)ÎRn´n, B= (bij) ÎRm´m are crisp M- matrices, C= (cij) ÎRn´m is fuzzy MATRIX and XÎRn´m is unknown, by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)´(mn) fuzzy system of linear EQUATIONs. Then, we convert this system to three (mn)´(mn) crisp linear systems of EQUATIONs, and we solve them simultaneously by ABS algorithm.

in this paper, differential EQUATION of sensitivity MATRIX of required velocity with respect to position vector is derived for a linearized problem of a spacecraft motion with final velocity constraint. This MATRIX can be utilized for an implicit guidance of a spacecraft with final position and velocity constraint. The solution is obtained in the presence of aerodynamical force. Therefore, the resulting EQUATION can be used for trajectory optimization. Moreover, a change of variable is presented to reduce onboard computational burden, in addition, the method is more appropriate for analytical approaches than conventional implicit EQUATIONs.