We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.

<p class="abstract"><strong>Background:</strong> In orthopaedic practice, three column concept and fixation for proximal tibia are becoming popular as it was proved that fixation of posterior column is a must for proper weight transmission and stability. This study demonstrates the use of the posteromedial surgical approach to the knee in treating patients with complex tibial plateau injuries with a posteromedial column fracture. The aim of the study was to study the functional and radiological outcome of complex tibial plateau fracture by posteromedial plating.</p><p class="abstract"><strong>Methods:</strong> This is a prospective study involving 20 patients with complex tibial condyle fractures with posterior column fractures. Preoperative computed tomography is taken with radiography for complete evaluation of fracture fragments even in the coronal plane. Fractures were classified as Schatzker type 4 or above with a posteromedial split depression. Plating is done with posteromedial locking compression for buttressing posteromedial fragment. The outcome of surgery was evaluated using the Oxford knee scoring system. Longest follow up of study is 2 years.<strong></strong></p><p class="abstract"><strong>Results:</strong> All fractures healed within 6 months without any secondary displacements or secondary osteoarthritis. Out of 20 patients 16 patients have the postoperative anatomic reduction (0 mm step off) 2 had an acceptable reduction of &lt;2 mm step off. At 4-12 months median range of flexion 135*(125-145*). The mean Oxford knee score was 25-33.</p><p class="abstract"><strong>Conclusions:</strong> Fixation of posteromedial fragment in a complex tibial condyle fracture is a must as it involves posterior column. Using a locking compression plate provides perfect fracture fixation and thereby more stability to knee joint &amp; better functional outcome.</p>

We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

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We have realized for the first time the multibreather vector multi-solitons supporting collision dynamics with many interaction effects (namely reflection, attraction, beating, etc., effects) associated with the coupled nonlinear Schrödinger family equations having multiple applications. Such effects can be suppressed or enhanced by using the soliton parameters. Here each colliding multibreather vector one-soliton is composed with many soliton and antisoliton parts. Our solutions have freedom to control the number of soliton and antisoliton parts used to compose a vector one-soliton with a definite breathing length. It is also interesting to observe that the breathing maps associated with the obtained solutions depend on their free parameters and also the system parameters. All such investigations help us to realize different breathing mechanisms (namely pedaling, toggling, symmetric compression, symmetric elongation, asymmetric compression, asymmetric elongation, etc.) supported by the colliding one-solitons. An existing breathing mechanism of a given vector breather one-soliton can be suppressed or switched into another mechanism by tuning certain parameters appropriately. Because of such features we believe that this kind of study will further give impetus on the Lindner–Fedyanin system in the continuum limit, and find the potential applications in fiber coupler and also in Bose–Einstein condensates.