Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

<div>Proportion scene of the solution equation (<a href="https://static.hindawi.com/articles/amp/volume-2018/9178480/figures/#EEq10">10</a>) with (<a href="https://static.hindawi.com/articles/amp/volume-2018/9178480/figures/#EEq13">13</a>) and (<a href="https://static.hindawi.com/articles/amp/volume-2018/9178480/figures/#EEq11">11</a>) for the values of arbitrary constants is <span class="nowrap"><svg height="11.6399pt" id="M30" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 191.258 11.6399" width="191.258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 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href="https://static.hindawi.com/articles/amp/volume-2018/9178480/figures/#EEq10">10</a>) at <span class="nowrap"><svg height="9.92533pt" id="M32" style="vertical-align:-1.57651pt" version="1.1" viewbox="-0.0498162 -8.34882 37.1536 9.92533" width="37.1536pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.065,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.328,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g 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(e-g) Consistent contour plot of (a, b, c), respectively.</div>

Advances in Mathematical Physics

fig2

Figure 2

Figure 2: Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model 