Decay Rate and Energy Gap for the Singularity Solution of the Inhomogeneous Landau-Lifshitz Equation on <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.3067999pt" id="M1" height="15.6075pt" version="1.1" viewBox="-0.0657574 -15.3007 17.6155 15.6075" width="17.6155pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-30" d="M597 536C514 627 443 676 315 676S72 616 72 475C72 255 443 260 443 129C443 65 375 30 319 30C204 30 143 77 70 158L35 130C115 36 196 -14 323 -14C443 -14 591 45 591 186C591 411 213 394 213 548C213 599 275 632 319 632C433 632 498 583 567 501L597 536ZM464 63C481 84 487 112 487 139C487 304 116 279 116 487C116 536 144 587 188 610L189 608C177 585 169 561 169 534C169 360 547 365 547 186C547 131 513 87 466 62L464 63Z"/></g><g transform="matrix(.012,0,0,-0.012,10.914,-7.578)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g></svg>

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Advances in Mathematical Physics

fig12

Figure 12

Figure 12: Decay Rate and Energy Gap for the Singularity Solution of the Inhomogeneous Landau-Lifshitz Equation on <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.3067999pt" id="M1" height="15.6075pt" version="1.1" viewBox="-0.0657574 -15.3007 17.6155 15.6075" width="17.6155pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g197-30" d="M597 536C514 627 443 676 315 676S72 616 72 475C72 255 443 260 443 129C443 65 375 30 319 30C204 30 143 77 70 158L35 130C115 36 196 -14 323 -14C443 -14 591 45 591 186C591 411 213 394 213 548C213 599 275 632 319 632C433 632 498 583 567 501L597 536ZM464 63C481 84 487 112 487 139C487 304 116 279 116 487C116 536 144 587 188 610L189 608C177 585 169 561 169 534C169 360 547 365 547 186C547 131 513 87 466 62L464 63Z"/></g><g transform="matrix(.012,0,0,-0.012,10.914,-7.578)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g></svg> 