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The purpose of this paper is to find out some new rational non-traveling wave solutions and to study localized structures for (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation.

Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation.

Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable.

As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.

With the help of the Lie group method, special transformations and the rational function method, new non-traveling wave solutions are derived for the AKNS equation by Maple software. These results are much useful for investigating some new localized structures and the interaction of waves in high-dimensional models, and enrich dynamical features of solutions for the higher dimensional systems.

The purpose of this paper is to find new non-traveling wave solutions and study its localized structure of Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation.

The authors apply the Lie group method twice and combine with the Exp-function method and Riccati equation mapping method to the (2+1)-dimensional CDGKS equation.

The authors have obtained some new non-traveling wave solutions with two arbitrary functions of time variable.

As non-linear evolution equations is characterized by rich dynamical behavior, the authors just found some of them and others still to be found.

These results may help the authors to investigate some new localized structure and the interaction of waves in high-dimensional models. The new non-traveling wave solutions with two arbitrary functions of time variable are obtained for CDGKS equation using Lie group approach twice and combining with the Exp-function method and Riccati equation mapping method by the aid of Maple.

The bisection inverse search bow height control interpolation (BIS-BHCI) method for nonuniform rational B-splines (NURBS) curve is proposed to accomplish the serial robotic plasma cladding of planar complex curve coating with high precision.

A plasma–computer integrated cladding system is constructed based on a Motoman-UP6 serial robot and a plasma power. Based on the BIS-BHCI method, combining the serial robotic kinematics with the NURBS curve model, an offline plasma cladding software is developed for Motoman-UP6. Before plasma cladding, a planar NURBS curve coating is designed and defined and its BIS-BHCI is carried out with proper parameters. Then, the cladding programs are generated using the BIS-BHCI results and the robotic kinematics and inputted into the serial robotic controller. After that, the plasma cladding of the planar NURBS curve coating is implemented based on the Motoman-UP6 serial robot.

The simulation and plasma cladding for the NURBS curve coating shows that the BIS-BHCI method is feasible and effective. Plasma cladding of complex NURBS curve coating based on serial robot is feasible and effective.

The complex NURBS curve coating is prepared based on a serial robot platform for the first time. It provides a theoretical and technical basis for plasma cladding to produce surface coatings of industrial complex parts. With the increasing application of complex parts, the plasma cladding process of complex NURBS curve coatings has a broad application prospect.