Ultrasonic focusing and scanning with multiple waves

This paper presents a new focusing and scanning method which focuses multiple waves on a target. The key of the method is to control excitation pulses for each element of the transducer array. The excitation pulse on each array element is obtained by time reversing the signal received by the same element, which is generated by an imaginary source at the target. The excitation pulses from all array elements are transmitted and arrive at the target simultaneously, and focusing is achieved. The performance of the two methods is compared in numerical examples, and it is demonstrated that the proposed method achieves a satisfactory focusing and a good signal-to-noise ratio no matter where the target location is.

Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the（2＋1）-dimensional Sawada-Kotera（SK） equation and（3＋1）-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota＇s perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.

An experimental study on runup of two solitary waves on plane beaches

Experiments of the runup of two solitary waves on a plane beach are carded out in a wave flume. The two solitary waves with the same amplitude and the crest separating distances are generated by using an improved wave generation method. It is found that, with regard to the two solitary waves with same wave amplitude, the runup amplification of the second wave is less than that of the first wave if the relative crest separating distance is reduced to a certain threshold value. The rundown of the first solitary wave depresses the maximtlm runup of the second wave, If the leading solitary wave is of relatively smaller amplitude for the two solitary waves, the runup amplification is affected by the overtaking process of two solitary waves. It turns out that the runup amplification of the second wave is larger than that of the first wave if the similarity factor is approximately larger than 15, which means the larger wave overtakes the smaller one before the waves runup on a beach.

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK)equation.The solutions obtained contain first-order,second-order,and third-order wave solutions.At the critical point,the second-order derivative and Hessian matrix for only one point is investigated,and the lump solution has one maximum value.He’s semi-inverse variational principle(SIVP)is also used for the generalized BK equation.Three major cases are studied,based on two different ansatzes using the SIVP.The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below,using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer,fluid dynamics,etc.

Multiple-order line rogue wave,lump and its interaction,periodic,and cross-kink solutions for the generalized CHKP equation

The multiple-order line rogue wave solutions method is emp loyed for searching the multiple soliton solutions for the generalized(2+1)-dimensional Camassa-HolmKadomtsev-Petviashvili(CHKP)equation,which contains first-order,second-order,and third-order waves solutions.At the critical point,the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one minimum value.For the case,the lump solution will be shown the bright-dark lump structure and for another case can be present the dark lump structure-two small peaks and one deep hole.Also,the interaction of lump with periodic waves and the interaction between lump and soliton can be obtained by introducing the Hirota forms.In the meanwhile,the cross-kink wave and periodic wave solutions can be gained by the Hirota operator.The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values.We alternative offer that the determining method is general,impressive,outspoken,and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.